Hmm, for me, it depends entirely on the game, I'd say.
In ARPGs - Having increased my skills far enough and got some fairly decent loot (I don't spend months farming for all the epic-epic stuff, I'm not
that obsessed

) to kill pretty much anything with ease...even better if I have the overkill to turn them into Ludicrous Gibs

.
In RPGs - Depends on the game, but similar to above - being powerful enough that I can stand against most things, get good prices in merchants, etc. If the game contains the ability to fly (or, in Morrowind's case, cross an entire large town in a single jump), that falls under the list of stuff that I try to get to consider myself "uber"

. These games, for me, tend to have the most satisfaction by the end, if the game is large enough and requires enough effort to become powerful, so I can feel like I earned it.
In games requiring stealth (the Thief games, Skyrim, probably some others) - Being able to go more or less wherever I want without anyone noticing me, and yoink all the good stuff. Dealing with guards and stuff. Never getting caught.
MMORPGs...or rather, the only one I ever played (EQ, back when I still enjoyed playing it) - As in single-player RPGs, having spent my time levelling up and becoming more powerful, gaining access to my class abilities so I can face down more powerful mobs without too much trouble...oh, and also go back and totally flatten the mobs that gave me trouble back when I was first starting out

. Also, having made plenty of friends during my time in-game, being able to log on and just sit and chat with them, join guildies in a group somewhere or help them/have them help me with a difficult quest. Being able to explore new places, either because I'm a high enough level not to get insta-killed the moment I go there, or because I have enough faction with the locals that
they won't insta-kill me the moment I go there

. Finally, because EQ actually required a lot of effort in order to do stuff back then, the "DING!" sound, especially at higher levels, was a whole level of special just by itself (undermined somewhat if you died soon afterwards and
lost that newly-gained level, but...well, you tried not to do that

).
In tabletop RPGs - Having some ability of mine do something really useful/helpful/silly/hilarous (whether I intended it to or not). Collaborating with my fellow players to put together some kind of weird (or even entirely practical) plan that ends up working

.
In co-operative card games - Okay...one
particular co-operative card game, in which you play superheroes of varying kinds, each of which has their own deck, and the object is to defeat the villain, who also has a deck (which has a card telling you what they do on their turn, so no-one plays
as the villain, you just need to turn over the cards and read what they say - all the players play as heroes) in an environment, which is another deck (automated like the villain deck) and which can help or hinder the heroes. the villain, or both. My favourite character is the Argent Adept, who's basically like an EQ Bard - his abilities are all basically "songs", powered by instrument cards, and involve doing a bit of everything - he can let other people play/draw cards or use powers, he can deal (small amounts of) damage, he can insta-kill
any card in the game (at the cost of sacrificing one of his instruments currently in play...and it doesn't work on character cards, ie heroes and the main villain...although funnily enough I've not used this one much, probably because there's usually plenty of more effective stuff I can do at the time), he can insta-kill environment or ongoing cards, and do a whole bunch of other stuff which generally lets the team work better, and has one of the more complex decks which requires you to plan and to look and see how all the cards interact, as well as look at what the other players have got available to them and which action will be the most profitable for the group, and stuff. Other heroes are versatile, but for me, he's
more versatile, because in a way he has access to the other players' decks as well as his own

. There are a couple of heroes (beside the Adept) who can let other heroes use powers - if a set-up Adept is present, it's usually a foregone conclusion that he's the one who'll get the extra power use, because he can use that one power to let himself use another power, to let himself use
another power, to let someone
else do some stuff, and...

Conversely to all this, what I
don't like in games is beating other people. I don't like PvP, in general. It's not so bad in
some games (I play Hearthstone a bit, for example), but in general I don't feel like I made someone else feel back by kicking their arse (or feeling bad myself if I'm the one whose arse has been kicked). It's fine if it's just a messing-around game, like some of the mini-games in Garry's Mod...though I've not actually played much of those because the graphics card on my computer died not long after I started playing. I need to reinstall it on my new computer at some point. Anyway, I've watched many Yogscast videos of it and it's hilarious...at least when played by a bunch of friends who all know each other and get on well and stuff

.
I also plan on staying well away from any kind of PvP once I get into the world of Elite: Dangerous (so far I have access to some single-player, combat-based missions, which I'm terrible at, but the Standard Beta goes live on the 29th which is when I'll be able to access what's so far accessible of the galaxy-proper). If people attack me without provocation, I expect I'll end up rather quickly changing to the "friends only" or even "single player" mode, depending on whether Ja'Ph' has got hold of the game

.
Anyway, there's probably plenty more I could say, getting specific to certain games, but I think I've waffled on enough for now

.