Let's talk about talking in RPGs. The TALK quarter of my BIG 4 things you do in RPGs is actually one of the biggest things in the 1990's era of RPGs. I point at Vampire (both versions) as the iconic talking game because social interaction plays such a big part. You fight, steal, and build empires, but at the end of the day it's you in front of the Prince trying to get him to see your way. (Unless you ARE the Prince of a city.)
Talking subsystems exist in a lot of games. One of the easiest to notice is any Honor or Renown mechanics. Werewolf, Legend of the Five Rings, Pendragon, etc. If you have a social standing and it impacts how you receive and ask for favors you are dealing with what I call at "Talk" system. This also includes contact and patron mechanics form games like Shadowrun or Cyberpunk 2020. Hell, even GURPS has a limited patron/contact system that while it uses more arbitrary rolls for 'frequency' and the like, it IS there.
Social subsystems that work tend to be pretty simple. A status/rank track and some method of knowing who you owe and are owed favors and alliances with. This can get out of hand mind you. Take Exalted 2nd Editions far to complex social combat. When you are tracking multiple SOCIAL actions in combat turns something has gone horribly wrong. A good talking system is something that works off of negotiation between the player and GM. It doesn't have to be "in character" mind you. The player can just as easy say I'm using contact X owed favor Y and I'll do him favor Z as well if he'll do this. The GM can roll and say that it meets the requirement of that contact and move on. Then depending on how things play out the players either gain greater or loss support. Simple really.
Another thing to consider is be open to taking social systems in weird directions. Shadowrun contacts can be everything from Street Docs to a Kid in an Orphanage if the players are out there schmoozing and making friends. Sure the kid might be able to get you cutting edge cyberware, but they might know where a body is found in the sewers. Don't be afraid to give the party NPC contacts that they wouldn't expect. After all, Sherlock Holmes got a lot more info out the Street Urchins he paid for information than Scotland Yard. The same goes in issues with other professions. Much like a Policeman's note book don't be afraid to have an NPC tracker for the party keeping tabs on folks you introduce them to. Use my Rule of Thumb on NPCs of these sorts and give them 1 or 2 distinctive features and be done with it. You can just hand them a sheet of NPCs they ran across in the previous sessions of you the GM are keeping notes.
Now some games enforce an economy of points, or exp to buy new contacts. But honestly past character gen I'd go the Shadowrun route and just let them build up a rating through interaction. GURPS and HERO's cost for favors works against GM spontaneity down the line.
Now in some cases especially in mechanics like Werewolf's Renown, make sure you follow the guidelines for rewards. You can adjust the rate based on speed of adventure/scenes, but I've found that most the reward values are set where they are due to previous exploits by players. (This is assuming that the system is playtested like say how extensively L5R's is vs...well. Quite a few others.)
Some Pathfinder games use a reputation or 'hatred' score count for PC actives. These while useful tend to be fiddlier than I like. They don't account for a wide range of possible actions and shoehorn players into scripted responses. When in doubt, throw it out and write up your own. Don't be afraid to do your own estimates on how high these values go based on YOUR game criteria. Note this is different from my take on Renown and Honor mechanics. The reason is these simple score checks tend to not be as robust as the previously mentioned mechanics. Mind you, if you as a GM feel like you can better judge Honor or Renown awards than the book and it works for your players. Go ahead. You're the GM.
Even in Dungeon World where the PC's have an interconnected story and the mechanics reward player interaction there is some level of TALK play going on. FATE handles it very well, depending on if the right flavor of aspects are being used. Don't be afraid to mix and match system if you can make it work.
Rewarding TALK players helps games. In old D&D terms the Cleric use to be the TALK character until the Bard was born, but even then the Bard is just a refined Cha focused variant on the more Wis based Clerics. Priest, Entertainers, socialites, holy warriors, and a LOT of business characters strive to make the most out the various social mechanics in play. If your group thrives on this level of PC and NPC interaction over combat and take/make game play make sure you are using systems robust enough to handle them. And make sure you as the GM are comfortable in the style of TALK play happening. Remember, don't be afraid to handle it as a casual exchange at the meta level of player to GM if "In Character" chatter feels weird. What matters is the result and how the story moves forward, even if it's in 3rd person.
Be chatty, make friends, have fun. Just remember to be polite. Unless...you know intimidation is your thing.
Diplomacy the M'F'ker.