Diplomacy is the IQ/H social skill for being or seeming reasonable at people. It lets you negotiate, make compromises, and generally get along with others. It's the hardest of the Influence skills, but it has major advantages over the other ones. It works as an Influence skill in any non-combat situation, allows a reaction roll as well as a skill roll and lets you use the best outcome, and doesn't alienate the target on a failure. You can also use Diplomacy to predict the outcome of a negotiating strategy, or choose the best course of action for negotiation. Overall, it's pretty good, and one of the characteristic skills of GURPS: no other game system I've played has something so useful, effective and safe.
Diplomacy defaults to IQ-6 or Politics-6, and Politics defaults to Diplomacy-5. It's a possible prerequisite for Group Performance, as an alternative to Leadership or Intimidation. Having Diplomacy at 20 gives you +2 to all reaction rolls, if you can talk, but this rule is a holdover from 3e, where achieving that skill level was considerably cheaper: 16 points bought Diplomacy at IQ+6 under 3e, whereas it now only gets you IQ+3.
Diplomacy modifiers are +2 for Voice, -3 for Low Empathy, -1 for Oblivious, -1 to -4 for Shyness, and -2 for Stuttering. Talking is clearly important, and
DF2: Dungeons makes it clear the skill is penalised for poor language comprehension. It also takes penalties for lack of Cultural Familiarity.
Social Engineering gives us more about Diplomacy. It's worthwhile for anyone who makes deals or other negotiations, and can often be a complementary skill. It works with text-only and voice-only communication, although obviously some of the modifiers won't apply. It can be useful in building loyalty and trust in a relationship, including employment, but is also the key skill for blackmail. Per-based Diplomacy is useful for finding the right people to approach for some purpose, such as the ones who know what's going on "round here".
Alliances and Diplomacy provides rules for negotiations between groups, with a lot of complementary skill options. Diplomacy can also be used to avoid fights, although once they're started it won't do you much good.
Diplomacy is extremely common on templates for characters who need to at least try to be reasonable, from nurses to kings. In the high-speed world of
Action, successful Diplomacy can get information from neutrals, or calm down a confrontation, and success by 5+ can get hostages released, or minor aid from neutrals.
Dungeon Fantasy has rules for negotiating with monsters, and manuals for Diplomacy, and
Fantasy has a section on diplomacy-based storylines.
Horror points out the usefulness of Diplomacy in convincing modern-day authorities that the problem is
demons, rather than teenage joyriders, and
Madness Dossier covers its usefulness in mimetic campaigns (and their drawbacks in the setting).
Monster Hunters has the same rules as
Action and
Dungeon Fantasy.
Mysteries has Diplomacy as the primary skill for interviewing witnesses, and allows modifiers for Reputation, Status and possibly Rank; getting through bureaucratic defence systems is the lower of Administration and Diplomacy. There are perks, quirks, talents and wildcard skills that use Diplomacy in the appropriate
Power-Ups volumes: the Influence Shtick perks are especially useful.
I've used Diplomacy a
lot in GURPS games, so much so that I don't remember incidents. It tends to remove obstacles in a less spectacular way than combat. Of course, sometimes that's
not the point in a game, but I'm happy to save firepower for when it's most needed.
What have you done diplomatically?