They most often end up as some scribbled notes on one end of some paper or the PC character sheets. Most often forgotten in a few sessions.I try to write them down at times so to celebrate their existance a little.
I have a stack of index cards for everything - locations, NPCS, weird rumors, and so on - and fill them out as things happen. I give the players a lot of leeway to add details to, so they also have stacks of blank cards and everything that isn't "known" gets added to cards. Then, when i get around to it, the wiki gets updated.
I note them and give them a little flesh for next time the PCs might encounter them. I have a progression, where first I give them a little better appearance and a roll on table 114B from Central Casting. Then, if they meet them again, they get the full seven sentences, and the next time, I roll up a background, which will have ties to the game world and maybe lead to more things to put on the map. This goes until I think I have enough for a full character sheet. The guys they've met a few times get rolls for what they do between meetings (I use stuff from the Mythic RPG for this). I run a sandbox, so I need to keep track of these guys and roll up plot lines the players can maybe follow.
I tend to the organized side of things...that's me. As Rev. Dr.Dale stated,index cards are good; the larger 4x6 index cards work well. Here's an article on NPC's you may find good reading that came out this morning after you posted this. http://www.creightonbroadhurst.com/?p=1003&preview=true
It depends on how the players react to them. I love having a recurring NPC or two that can act as my mouthpieces to get players information. But if the players have no interest in following up with the sullen armorer they purchased their armor from, I don't bother with it either.
If the NPC lives more than one session and I also remember (and care) on the second session enough to keep him relevant then yes, I formally turn them into some sort of write-up. It used to be really important when I had a group that was smaller (3-4 players) who were absolutely obsessed with henchmen, contacts and lackeys. At one point we had a roster of retainers 40 strong and everyone of them had a personality and short history. My current groups...not so much, at least partially because these days I'm lucky if I only have 6 players at the table, so NPCs get less "floor time" to keep things moving.
I remember them with my brain.
What Jim said. I try to keep the more memorable ones around and I think I'll add the index card idea to my list of things to do, maybe one of those spiral bound index card mini-notebooks. I do dislike the idea of not having them electronically (where I could sort them and search them easier), but keeping them even in an unorganized fashion is better than letting them disappear into the ether.
The same way I handle random encounters and monsters, everything is a potential threat to the PCs' safety and status quo. NPCs get names and desires, I write those down and then I just see what happens, if I need stats I make them up on the fly.
I keep a notebook for each game, and I write down all the names I use. I date the entries by the real date, game dates, players who showed up, etc. and use it for all my notes. So improvised NPCs, fun quotes from the players, HP/damage tracks for battles, etc. - it's all together. Having that means my improvised NPCs get to return, easily, and it's only a page flip or two back to determine, say, who the barkeep is at the inn, or whatever.
In the last year or so, I've been keeping a couple of Gamemastery NPC face-card decks on hand for this very purpose. If an NPC makes a return or recurring appearance, I pick out a card and scribble some notes (or update them) on the back of the card for the next session.
If players seem interested in an improvised NPC, I develop him or her a little between adventures. If the players don't care, then neither do I. Most things I just remember, rather than making formal notes.(I do tend to slaughter NPCs in large numbers, but it's not because I don't want to keep track of them. I just enjoy doing it.)
Sometimes yes, sometimes no. I usually make a quick note, especially if it's in a location the PCs will be spending time in.
If an NPC is likely to be sticking around, try to imagine which actor would play them. This makes it much easier to be consistent with their mannerisms if that's important. So, for example, if Mungo the Merchant reappears you know he's like Harvey Keitel and as for Boris the Bard, he's Kevin Eldon as Tony Rudd (YouTube it!) but with a sombrero.Naturally the players don't need to know any of this and, unless you've chosen Clint Eastwood or Sean Connery, the chances are they never will.
I have a single sheet of paper with a list of pre-generated names on the left column, blank space on the right. When there's an improvised PC, I just write down the PC's detail next to their (newly acquired) name. That leaves me with one page campaign notes. I think it might be a little easier to keep track of and deal with during than a stack of note cards.
It really depends. If it's an NPC with whom the PCs have minimal interaction before moving on, then the NPC just fades away statless and noteless. If it's an NPC with whom the PCs do interact significantly, then I make notes (usually right after the session) and I develop the NPC a bit more.
For me as a GM, NPCs are where it's at. I spend a lot of the game interacting with the PCs with NPCs and while I do a lot of improv with them, I usually have stuff written down. Rarely do I have a character querk that I do not recall (althoguh I will screw up an accent sometimes)