Personally? Not really. Most of my gaming history, social competence is "invest in this die roll", be it Charisma + Diplomacy, Charisma + Persuasion, the half dozen or so relevant social abilities in OWOD, etc.. When I play, you roleplay, and if the GM decides the NPC wouldn't give you something for nothing, you make a die roll.
And online in forums, for decades, I've seen a lot of DM's who are very resistant to social systems. There's much talk about what players shouldn't be able to get from success, what things should be taken off the table, how DC's are too low and it's too easy for players to succeed. Many claims about wanting social interaction to be more interesting, but most of the actual discussion is how to prevent those dirty, dirty players from getting what they want. The DC's go up, the players bonuses rise, "Bluff is not mind control" because no matter how easy it is to trick people in real life, somehow NPC's cannot be easily beguiled, and eventually you hear horror stories about players who just give up and start using magic to bypass intractable NPC's, lol.
I think pointing out where the problems are helps point out where the solutions are. Here is the system I’ve been using, though other posters have proposed others.
Point 1: In many respects, social systems can be more flexible than combat systems.
I don’t use my social systems for all encounters. You want to haggle with a merchant for a discount? Just roll Persuasion.
Convince the king to abdicate and name you successor? He’s not going to do that. No roll.
Conversely, most DMs don’t skip over an uninteresting combat with a single role, and allow the party to play out several rounds of an unwinnable combat.
Which leads to…
Point 2: when to use a social system.
I only use my social system if it makes sense to spend an hour or more in game on the encounter and if the encounter has several possible interesting outcomes.
Point 3: multiple interesting outcomes
First step is setting out interesting outcomes. Generally, there should be at least three, but I try to aim for four: worst, bad, good, best (I don’t like to use failure or critical failure, because even “worst” can be success at a high cost).
Point 4: the social encounter
As a poster pointed out, combat can use multiple rolls because the stakes on each individual roll is low. I apply this to social encounters as well.
In contrast to combat encounters, I tend to have a set number of rolls for social encounters (depending on the size of the group, 3 or 4 per person). For the sake of simplicity, I set good at the 50th percentile of total rolls, and bad and best at 25th and 75th respectively (you can adjust if necessary, but the main challenge to the players comes from setting DCs).
Unlike 4e, an important point is that failing a roll does not impact overall success, unless your actor’s actions would obviously and immediately do so (like attacking the NPC). This means that even less socially adept PCs can involve themselves, and are in fact often more willing to try unconventional tactics, because they are less likely to succeed with spamming Persuasion rolls.
Point 5: being unconventional
Ahead of time, I identify 6 or 7 skills or tactics that succeed. I also make a note that any clever tactics by the characters has a chance of success (or even counts as an automatic success).
I use some tactics to make multiple rolls less interesting. One, the “anytool” skills (Perception, Insight and Persuasion) tend to have higher DCs than skills that are more specialized (that art critic is a lot more likely to care if you discuss recent developments in the art scene (Performance) than if you simply butter them up).
Here, as a DM, be unconventional. You can, because the individual stakes of each roll are low. In addition to skills, the characters’ tool proficiencies, languages, Background, Personality, Bond, Ideal, Flaw and beliefs can play a role in the social encounter.
