You roll a 3...

[Celebrim]

In most editions, strength, intelligence or charisma are dumpable stats. Which you choose would depend on what you'd want to play:

1e/2e: Dump charisma, play anything but a Paladin (1e) or Bard (2e). You'll never have a retainer and you'll be dependent on the party for all social interaction, but other than that you're good. You'll even be able to save your party from a horde of Korreds.

UPDATE: I'd forgotten some of my more obscure 1e rules. If you put the 3 in Charisma in 1e, you can only play an assassin. Since the thief and assassin lose much of their charm by 10th level, you're better off putting the 3 into Intelligence and playing a fighter or putting the three into Strength and playing a Wizard. This probably means that even in 1e, the option of playing the low strength Wizard is probably your best choice.

3e: All three options are open.

Dump Intelligence: Play a fighter, barbarian, druid or sorcerer. This should work fine in a high magic game with low skill use.
Dump Charisma: Play a fighter, barbarian, druid or wizard. In some ways, even better than in 1e because retainers are less important. Might not be completely without penalty in a high skill game with a DM that forces players to make individual social checks, but in many games you'll feel no pain.
Dump Strength: Play a Wizard or Sorcerer. The safest choice in a game where you know the DM is fond of a lot of skill checks. You'll be more useless than usual in a fight at low levels, and you'll have trouble moving around the dungeon even naked but by mid to high levels you'll probably barely notice the penalty.

I'd probably take the option of Wizard and the attribute array:

Str 3
Dexterity 17
Constitution 18
Intelligence 18
Wisdom 16
Charisma 14

Elf, Dwarf, and Human all look viable to be. I'd probably play Human, but the idea of either 19 Dex (as elf) or 20 Con (as dwarf) is very appealing. In all three cases, this character is likely to overshadow the party in the long run, being the equivalent of like 50 point buy. With high AC for a wizard, hit points equivalent to some fighter types, best possible primary attribute, and more than I need wisdom and charisma, grappling is basically the only thing I'm worried about, and I can take care of that by proper spell selection and/or item creation.

 

[Dausuul]

In most editions, strength, intelligence or charisma are dumpable stats.

Any reason not to dump Wisdom in 1E/2E? For that matter, you can dump it in 3E if you have access to Force of Personality.

Dexterity is usually a poor choice to dump, and of course you never want to dump Constitution. (You can get away with dumping Constitution somewhat in 4E, but dumping it to 3 would be rough in the early game--you lose too many hit points.)

 

[Ahnehnois]

I could see a great character with 3 Con who's dying of cancer or something like that.

That being said, I'd likely put it into Dex and play a spellcaster, I made an illusionist like this once who always kept himself hidden behind a spell.

Frankly, the only mental stat that's really playable at 3 as a 3 Wis character with some severe mental illness. Charisma has little statistical impact, but playing a 3 Cha character correctly-i.e. he can barely communicate for some reason-is generally not much fun. 3 Int is also really hard to play properly unless you have another character to advise you.

3 Str is fine except for low carry weight.

 

[Celebrim]

Any reason not to dump Wisdom in 1E/2E?

Well, -3 on saving throws versus mental attacks isn't particularly fun. Plus, you can only play a thief.

Which raises the point that with a 3 charisma in 1e, you can only be an assassin (which I'd forgotten). So in 1e, your valid options are pretty much only dumping Strength and playing a M-U, or dumping Intelligence and playing a fighter.

Obscurely, dumping wisdom rather than charisma reduces the relative chance of being psionic as well as makes you more vunerable to psionic attack (including psionic blast). If you dump wisdom, chances are the first encounter with a mind flayer will be lethal.

In 3e, dumping Wisdom almost always results in more enemies gain surprise against you as you fail spot/listen checks, so dumping wisdom is generally never a great option even if you have feats that mitigate some of it's other problems.

 

[JRRNeiklot]

Dropping strength to a 3 is a bad idea. This leaves you with a weight limit of 150. Your spellbook probably weighs more than that. Charisma is probably the best choice, followed by int or dex. A 3 dex cleric is very playable. I'm currently playing a cleric/mu in a 1e game with a 7 dex.

 

[Celebrim]

I'm currently playing a cleric/mu in a 1e game with a 7 dex.

A 7 in an attribute in 1e is roughly as 'crippling' as a 9 in an attribute in 3e. It's a very minor penalty, so I would expect characters with a 7 in something to be very viable.

A 3 in 1e on the other hand is usually very crippling. While the 3 dex cleric is probably somewhat viable, the -3 reaction adjustment is surprise situations is lethal in the extreme, and the +4 penalty to AC is pretty much going to negate any advantage you gain as a cleric in the ability to wear armor.

To give you an idea how bad a -3 reaction adjustment is, understand that in 1e it means when you are surprised that you are effectively subject to 3 extra surprise rounds. A surprised dex 3 cleric is potentially subject to 6 rounds of attacks before they can even attempt an action. I just don't foresee a character with a 3 dex ever surviving being surprised even once.

 

[Dausuul]

Dropping strength to a 3 is a bad idea. This leaves you with a weight limit of 150. Your spellbook probably weighs more than that.

That's what fighters are for. At low levels, you'll die without the fighter anyway, so why not let her carry your spellbook? At mid- to high levels, you have other options available.

 

[JRRNeiklot]

To give you an idea how bad a -3 reaction adjustment is, understand that in 1e it means when you are surprised that you are effectively subject to 3 extra surprise rounds. A surprised dex 3 cleric is potentially subject to 6 rounds of attacks before they can even attempt an action. I just don't foresee a character with a 3 dex ever surviving being surprised even once.

What surprise? That's what rangers and monks are for.

 

[Dannyalcatraz]

Really, if you think about it, you can dump any stat you want and still have a fun and long-lasting PC...especially if it's the only bad stat you have. Not only are there viable options for each "void" stat, there is the fact that most campaigns have more than one player. Whatever weaknesses one PC has, another can probably shore them up.

Try running a game with 6 PCs, each with the same stats to arrange, but each dumping the 3 in a different stat. Characterizing roughly, you'll have a weakling, a stumblebum, a scrawny twig, an impulsive twit, a moron and an ugly jerk.

You may also find you have a powerful arcanist, a great healer, a clever trickster, a fearsome Northman, a paragon of humility & virtue, and the greatest warrior of his generation.

 

[Celebrim]

What surprise? That's what rangers and monks are for.

Reduces the chances for surprise but not the severity of it when it happens.