When I build a character, I almost always find myself putting tons of points into evasion. My next priority is accuracy. My game philosophy: being the strongest guy in the room doesn’t matter if you can’t land a hit, and visa-versa.
Of course, some games combine evasion and accuracy as agility or dexterity or some such (or in the case of Kingdom of Loathing, moxiousness). Which is pretty awesome as far as I’m concerned.
Int – but then I play wizards. However, it really depends on the stat system. In Dark Souls while Int is still my primary stat, Endurance is a very close second (I don’t bother with vitality in that game since my experience is that it’s better to learn to avoid getting hit than to worry about when you get hit – and most of the time vit would be important an estus flask works just as well except in extremely rare 1HKO cases).
Of course, there are some bizarre exceptions, in Tales of Graces Aim and Evade are basically the two main stats for everyone, and everything else is sugar.
ETA: And in Warcraft III, in Custom maps where you had a choice, an AGI hero was basically the only one worth mentioning because ridiculous +AGI basically made you invincible.
The stat that allows you to resist manipulation, intimidation, or fear. Charisma in some rule sets, composure in others.
Depends on the game and character class. In WoW, for example, a warrior does not need INT, and a mage does not need STR.
If it’s a video game RPG I’ll typically put points first into whatever stat unlocks the most dialog options. So Charisma or someshit.
In tabletop games I tend to play characters with high intelligence/wisdom/whatever.
I WOULD do that, but I’ve found that in the majority of CRPGs I’ve played, you can basically get 99% of dialogue options without high charisma. At least, my mage in NWN (and NWN 2) had basically no problems with diplomacy checks except in maybe one or two rare cases.
ETA: And in Planescape, there were tons of options that were linked to Wis or Int over Cha. Hell, in NWN2 there were a lot of dialogue options opened by the SPELLCRAFT skill of all things.
I always liked to work on a nice set of support skills. Stuff like healing and analyzing magic and languages and picking locks. Let the “meat shields” do the fighting.
Cha. No matter what my main stat is, I’ll have good Cha. (14-16, unless I’m going for a particularly charismatic (not necessarily Cha-based) character, in which case 18+.)
Str/Con based? Big, burly, and VERY good at making you think they can and will break you - so they don’t have to bother actually doing so.
Int based? People listen to them talk, rather than writing them off as a nerd.
Wis based? Well, I only do Wis-based (as opposed to simple high-Wis) when playing a D&D Cleric, so why they’d want high-Cha is obvious.
Dex based? They’re lithe and pretty, as a consequence of being all dexterous. Also, usually very likeable goofballs.
Being Really Damned Pretty is also a valid alternate or addition to any of the other ones, as well. Or Really Kinda Odd-Looking. I tend to want characters who are interesting to look at, be they big and ugly, slender (or zaftig) and beautiful, or look like an Egyptian deity. So, high Cha, FTW.
Sanity. You can’t have enough Sanity.
Usually Strength, because it’s often necessary if you want to carry a lot of equipment (not to mention that melee attacks often require less hand-eye coordination than ranged attacks, depending on the game).
Chutzpah
Derail!
Really? What do they DO? I honestly couldn’t tell, and the game never explains it. In a game where, as far as I can tell, there are no “computer determined” hits or misses, what purpose do these stats serve?
For the win.
(It’s a stat from the old “Toon” RPG, by the way.)
I prefer to take Regeneration or Recovery or whatever attribute that lets the character recuperate from hits and fatigue faster. I hate waiting around or using consumables to get back to full capability. And it’s even better if the stat works during combat. I had tons of fun with a Regen Scrapper in City of Heroes. 
Yep–and wasn’t Moxie also a stat in that system? Or am I thinking Paranoia or something else?
If you’re asking what stat I tend to bump, it’s usually intelligence or wisdom: I love to come up with weird plans and to solve mysteries, and I figure I need one of those to justify my character’s actions.
But if you’re asking my favorite stat for its sheer existence, it’d have to be White Wolf’s key stat in its Wraith game: Angst.
This is what I came into post.
Further in that vein, Edge (Shadowrun), Moxie (Eclipse Phase), and similar stats. I love having a stat that–every once in a while–allows you to say, “Screw physics. I’m going to do this because it’s awesome/funny!” They enable you to trigger critical successes, reverse the outcome of bad dice rolls, ignore penalties, automatically go first, and the like. I think of them as representing your character’s ability to trigger a kickass cutscene.
In games without a Cinematic stat, my preferred stats vary with the character. I generally like defense/evade/armor class, though. Not getting hit is nice. I also tend to bump up intelligence; I don’t like to play dumb.
Magic item find. Magic begets money. Money can usually buy anything else I might need.
aka Lockpicking in some games, or Do Technical Stuff in others.
I always preferred to play a noble.
What? Traveller was a perfectly good RPG.
Given the way my 3.5E game went last night, I’m going to have to say that for sheer joy nothing quite beats “bonus to grapple checks”.
–Zeriel ended up breaking that dragon’s wing before it saw eye to eye with me on who was in control of the situation.
+1. It’s even more useful if you’re playing in the Solomani sphere - where it makes you a Party member - or among the Zhodani - where it unlocks psionic powers.