But I'm Always the Healer!
Some people just like to heal, that's all. It's not weird, it shows they care about their fellow adventurers. These players reveal themselves (steady!) pretty early on. They'll introduce themselves as a herbalist, or apothecary, or some such, and will have a quarterstaff instead of a big lump of metal on a stick. Their character sheet will be filled with the names of plants, like lesser snortweed and hairy marsh tuppence, which they'll grind up and rub all over you at the first sign of a paper cut.
Looks Like an Elf, But it's Not an Elf
These players are difficult to spot at first, because they will have told the GM to keep their real identity/species/gender a secret. Some people just like to take the alternate identity thing and give it just one more twist. Of course, the group will eventually discover the truth, maybe while bathing, when arrows seem to bounce off them, or when that suspicious bulge in their pants turns out to be a tail. No matter, there's always a new character to roll up!
I Need Protection!
I can't really say I blame people for doing this, as pretty much every game world is dangerous. But for these players, they can never have enough armour points. They're already wearing full plate armour forged by dwarven smiths out of Smaug hide, carrying a shield made from a bank vault door, and all blessed by the gods themselves to resist anything. But then the party find a ring of protection that gives the player +1 more, and they're right there, explaining to anyone who'll listen that it makes the most sense, for the party of course, if they have it.
A Call Five Arms
I'd imagine this happens to most players at one time or another, it's easy to lose track during an exciting game session. But this player makes a habit of it. Off they go down into the dungeon, dual-wielding a sword and dagger, with a shield in one hand, a lantern in the other, and a map in the other, like a freaky Swiss army knife made of flesh. At some point the GM will challenge them on it, but they'll soon go back to their old ways.
I Might Need it One Day
This is more of a long term thing, and many characters are burdened down at the end of a campaign. But some players just let their character keep everything they've ever owned. A look through their character sheet will reveal a list of the stuff they’re claiming to carry. Every set of armour they've ever owned, every weapon, every tooth/claw/kidney from every creature they ever killed. Remember that time when they thought they'd found a magic stone that was actually just a stone? Yep, still got it. This is why it's a good idea to have new character sheets every now and then.
I Can't Use it Now, But...
Whenever the party find anything useful, this player is at the front of the queue to take it. No matter what it is, whether they can use it or not, they want it. If the party found a magic helm, for instance, this player would be there trying to get it, even if they already have a magic helm, and the new one isn't as good. “But I might lose this one, or break it, or I might grow another head, I just want to be prepared.”
Everyone gathers stuff along the way. At the end of a long campaign, character sheets can get a bit messy. But this player takes it to extremes. Most people manage with a printed character sheet specific to the system they're using, a blank sheet to take notes, and maybe one or two notes from the GM. The librarian's character sheet is like a novel, several sheets of paper joined by a treasury tag, with every map, clue, name and place they encountered along the way. In addition, they have little notes attached to the tags, flapping around like elf-ears in a gale, usually so far out of date even the GM doesn't know what they mean.
Who's This Guy?
You've slogged through the Marsh of Death, climbed the Tower of Fangs and are finally ready to face the blackest of black mages and his horde of undead kangaroos, (What? Kangaroos are scary!) to rescue the prisoners and retrieve the Book of Powerfulness. Just before the first dice roll that will start the combat, this player says “What are we here for, and who's this guy?” and you have to pause while someone explains it all to them. Different players have different levels of immersion and dedication to the game, which is only natural. This player is mostly here for the social aspect and the beer.
Jack of All Trades
As I mentioned, this is most of my characters. I just like to get stuck in, ok? Whatever the situation, I want to be involved. Combat? check, big axe. Scouting? check, sneak skills. Magic? check, fireball! Healing, picking locks, identifying footprints, line-dancing, making chimichangas? check. Ok, this approach, to complete the quote, does make my characters '...master of none' but I'm not bothered. Ok, so I have a one percent chance of understanding what the foreign merchant is saying while lip-reading in the fog, it's better than none at all.
I Look Under The Fire
As many RPG worlds are magical or technologically advanced, many things are possible. It often pays to be thorough. But this player isn't happy until they've looked absolutely everywhere. For instance, if the party were searching for the resting place of a vampire, this character would be looking in buckets and under tea cups, because “you never know.” The rest of the party have already stopped searching this particular location, because the GM said, very slowly, “you don't find anything,” which most players know is metarule code for “there's nothing there, let's move on.”