Things to Roll...
Administration: roll to stretching resources farther beyond their current capacity. Failure, just means you cannot stretch it any farther than your current range. Critical failure means mismanagement.
In a game, I used administration for the player to "hide" his paper trail, a -5 task difficulty to compound the difficulty of someone attempting to track it. (all paper work can be traced, the time it would take though is what you're really attempting to buy with the roll).
Intelligence Analysis: Convert Raw Data to Simple Player-Friendly Information (secret roll). GM will give bad info in a really bad roll (usually at margins of 5 or greater).
Strategy: The GM rolls to Highlight more options or the best Available Options (secret roll). The GM can provide bad data in a really bad roll. Personally, Major Decision are a Player-Only matter and Strategy should Aid the player and NOT-do the player's job. Also, no plan survives first contact, even the best possible strategy roll.
Literature (popular or folk lore):
Soldiering: Adds to Fear Checks when Discipline would matters. Knowledge of all the common and uncommon risks of the job, as well as familiarity of how to negate those risks. Soldiering skill bonus gives a lot of advantages and the fact so many rolls are default-able to soldiering that no more reasons could be cited.
Savoir-Faire: This is basically the skill to show respect, courtesy, and present the best "appearance". Sincerity of Respect essentially what is communicated by this skill. The timing and candor of a salute, knowing which chair to sit in, what fork to use, how to compliment a dish etc. All this is very cultural but is what is part of the Savoir-Faire skill (which I tend to simply call etiquette). Even common people have the Savoir-faire skill, showing "respect" can be taken for granted but is the foundation of basic manners. Of course, some-people are ingrained to constantly use certain etiquette which becomes a disadvantage when presented with a different culture. While some people may already expect respect, Sincerity is another element the skill can offer.
Animal Handling. Simply the ability to make an animal do what you want it to do. TDM +0 for trained animal but unfamiliar to you. TDM +5 if it is an animal you trained and it has been trained in the trick. TDM-5 to -10 a wild animal. Dogs, Horses, and Falcons are common Animal handling skills.
Math (Applied). Also known as Arithmetic, TL3 characters don't get as much practice as us and under time pressure there are a variety of problems that one can think of that being knowing one's numbers is more than handy. In every Merchant transactions, give a -3 to -5 when there are high values involved. You can use this skill to substitute for Accounting when making sure relatively small figures are added correctly. Accounting is more specialized for organizing and juggling more raw numeric data. If the task is personal accounts, roll Math, when dealing with an Army's ledger use accounting to add up sums. Suffice to Say, Narses a Eunuch general who was a Palace Steward, must have depended on his organizing skills (administration, accounting, math, intelligence analysis and strategy) in running his army instead of his credibility as a warrior or favor of the emperor.
Farming. Growing things, identifying raw food materials and their quality, appraising the state of a small community (since ALL small communities are agricultural in nature in Low tech). Its a skill that lets a character get along with farmers, use Farming to talk shop and as an influence skill. "my father would plant blah blah blah..."
Noble background. All the skills you see in noble background, come in play in any social event. A celebration will have dancing, audience participative-entertainment, and carousing. Without Any of the skills present, means the PC seen as a dullard, not part of the crowd and basically singles himself out. Celebrations are important in the REAL world, they are usually religious events and intended to manage populace morale. Gossip (aka Intelligence), contacts, and future endeavors are made by such gatherings because they are important enough to make people leave their far flung self-sufficient estates.
Psychology (Applied). Check out the description of the skill. All thinking characters actually have this skill. Consider that if you used Strategy to determine your enemies options and his best strategic option, then used psychology to use his pest "personality" option, a PC can do a lot of damage. This is always and SHOULD be a secret roll. I find this just too good to allow players the access of being Dead certain of the roll.
Roll against skill to predict the general behavior of an individual or small group in a particular situation
Housekeeping. Low tech house keeping has a ton of chores that makes a family relatively self sufficient. Like Administration, this skill can be used to best utilize domestic stretch resources for guests, or Impress peers or their masters.
Cooking. Low TL cooking has A lot of skills modern times have taken for granted. Knowledge of edible herbs and mushrooms are part of the skill. Preparation of secondary, anciliary and emergency food groups to make edible is also part of the skill. So a Survivalist better have cooking if he hopes to make that near toxic food he found edible. It would be quite exciting when survival or death can be made with such a under-estimated skill like cooking.
Navigation. Path finding, the needed to get from A to B (secret roll). A very important skill in adventuring, in fact an indispensable skill. The default Time is calculated by take the distance and multiplying it by the terrain difficulty factors (x1.5 to x3). A good roll allows the PCs to take the most established or safest (with the best watering points) route (not the fastest), A margin of success of 5 or more will maybe save 10% off the travel time (critical is saves 20%) by finding some time shaving shortcuts along the main path. A margin of failure by 5 is basically double time spent. critical failure is lost. A player who wants to risk a path can ask the GM for a voluntary penalty like Haste actions in B346 (-1 = -10%). Note that moving through difficult terrain doubles or triples travel time, the most efficient path can never be faster than time it would take traveling the distance in a straight level road. Path-finding, Land Navigation is an awesome skill, since victory and defeat can be made just by time alone.
Survival. Survival checks are also secret rolls, because typically they are made to avoid natural hazards. Typically you only know you failed a Survival check, when your already IN the deep trouble.
Survival and Camping. Survival checks are also important for knowing where best to lay camp. This roll is important at night or when there is poor light. Judgment of a good camp depends on the amount of information at hand and the situation of the players.
Survival and Water. Survival is an active roll when the PCs are looking for water. Enough for themselves can be found along the way in tiny alcoves where the survivalists will collect the water for drinking of the next day after they can boil and clean it. Typically with easy to find naturally occurring anti-septics and by mixing in some wine (and possibly honey or beet sugar syrup) with the water when boiled. Failing by 1 or 2 may lead to some bad water or some hard water substitute (like high water content roots or stems that need to be laboriously prepared at night). Failing by 5 means either water that takes a little more than the usual amount of processing to be drinkable (roll HT!). Remember that foraging for water is much harder when you have to drink more, -2 if your foraging for a horse, -5 for 3 of them, -10 for 7 of them. Note that Main Roads have watering points (thats why they were main roads), like artificial or natural ponds, streams or brooks. Seasons and the Region's unique traits affect these rolls.
Theology. Theology is important because it may give the best religious guidance possible in a time. A PC can interpret messages or signs, cite scripture, for the best course of action. A Theology roll can allow the PC best manage a uncertain situation by allowing him to beseech the proper deities or their representatives (invoking the right saint), know the best or proper offerings, and determine the message of an omen. Basically it is a Morale and uncertainty management skill, it provides the best suited religious answers in a given situation that would best ease the fears of the PC or a crowd. Another more impressive use of it, is its use in religious debate and interpretation. Religious knowledge can Awe, shock, Shame and Rebuke individuals (used with Public speaking, intimidation, diplomacy, or fast talk) among those who don't have their priorities in the religious; use the average of the skill (public speaking + theology; fast talk + theology etc.). A character unequipped with theology will be brow-beaten by others who are equipped with it, when this ignorance is seen.
History (local): Just as good as Area knowledge, but has more connected topics. This skill can impress locals, allow for a better grasp of the political layout, and a bunch of usefull things depending on the situation. Knowing the history of one's home region, always turns up interesting and useful tidbits.
Diplomacy. Saying something politically correct, double talking, or saying something that can be left to the targeted interpretation of the listener is one of the FUNDAMENTAL tricks of diplomacy. Understand that there is a HUGE spectrum for Point of View, and Diplomacy allows a character to safely navigate that spectrum. Basically it allows the character to Say what he means, without being mis-interpreted or his words twisted to be used against him. Roll diplomacy if the Player wants to say something shielded by His PCs diplomacy (optionally secret). Diplomacy is also a weapon allowing un-shielded or shielded discourse to be twisted into something else.
In my personal game view, social rolls are meant to augment Player's abilities and not do the Player's job in the matter of conversation or intelligence gathering. That just takes out all the fun from role-playing the interaction. Give the players the safety net of their character's social graces.
Politics. Politics in the GURPS definition is basically Popularity or Publicity skill if you contemplate the RAW meaning. BUT my use of the skill, is basically as an Organization Tool, being political is the skill in being in the good graces of certain people (a juggling act of keeping as many people happy or up in the air). Almost every major action is political, you can choose to Roll Politics when your making waves to "manage" them and make sure they have the most recoverable backlash. Ideally the GM doesn't roll this skill, he basically makes the skill a form of "Damage Reduction" adding a level of precision to the PC's overtures. Other Non-political PCs suffer Backlash, political PCs suffer less backlash for their actions. The GM and the Player can think of "after-the-fact" excuses why he wasn't hit by as much backlash.
Acting. This is the GURPS skill needed to Lie convincingly. It is also the skill to guard a PC's reactions (vs Psychology, Body Language, and detect lies). A poker face also takes Acting, but as a WILL roll (or a Fearlessness Roll for intimidation). A character without acting is an open book to expert social animals, the default penalty of acting (-5!) makes it a skill that cannot be easily ignored. In a recent discussion in the boards, acting is used to "pretend" not to be looking at something. Surprisingly Acting has too many good uses to ignore.
Packing. Have you ever packed for a trip? Packing IS a skill of organizing and efficiency, a character with packing can squeeze in more things than a person without it. While administration can be used to keep army logistics going, Packing is for Personal Logistics, any ranger or trekker who doesn't know how much he can carry efficiently and how best to carry it, will not get from A to B in one ideal piece. Roll this to squeeze in more equipment beyond the basic encumbrance and Bulk levels. This also allows the PC to take care of pack animals.
History (war). Like in Sherlock Holmes, and many detective stories: "nothing is original". There was always something like it, or happened that is close enough. History can act an intelligence skill, interpreting data with the aid of historical precedence and patterns. As a last ditch, Characters can always look to history for insight to a problem. If a character is making an military operation roll (Organizational, Intelligence, Strategy or Tactical) and fails by any degree let him re-roll with History at -4 as a second chance. This provides an incredible buffer against absolute failures. This should be allowed only once per scenario.
History (family): Part of establishing ones self as part of a peerage, one tends to need the pedigree to pass. Family history establishes legitimacy through the line of long dead, glorious or inglorious relatives. TDM easy tasks (+5) to remember the most notable, TDM -5 for the most obscure and secrets. Practically, this skill is useful in establishing legitimacy and precedence for a bunch of useful actions. This acts in the same way as History (war) for Political matters because by extension of one's own family, the character learns of their relationship with other families.