This depends on a host of factors.
The first thing to consider is what rulebooks are you using. Next you need to consider what ability score method is being used. Third the level you're starting at. Finally, the context.
To start I'll assume Player's Handbook, 3d6 in order, level 1, campaign play.
When you're doing 3d6 in order, it's really the dice that determine the class and race combination to - you need to pick what's optimal to increase your survivability.
If we make one tweak, and take one of the alternate rolling methods, like 3d6 6 times for each stat and pick the best one, you get a few more options. At this point multiclassing becomes a good option.
Another variation would be 3d6 arrange to taste, or 4d6 drop the lowest, arrange to taste. Here you might get one or two high scores. If your highest score is 13 or 14 a good choice is Cleric - you get good armour, Splint Mail puts you at AC 4, good weapons - Mace and Flail are always a good choice, and you get 1-2 bonus spells, making you among the most versatile characters possible.
If you've got scores in the 15-16 range, especially more than one, some of the other classes become viable. Thief with high scores in Con and Dex gives you a boost to hit points as well as AC on top of a boost to your regular thieving abilities.
If you're hitting 17-18, and especially 18, then Fighter and Wizard become some good options. Fighter thanks to percentile strength, Wizard thanks to having a good chance to learn spells and the potential to cast 9th level spells (if you start at 17, you'll probably get an age boost to 18 at some point).
Obviously the Cleric still benefits from higher scores as well, but is the optimum choice in the 13-14 range. Thief and Cleric are both options in the 15-16 range and all the base classes are good options at 17-18.
If you're stuck with 12 or lower, strangely the Thief ends up the best option. A Wizard is useless, a Fighter can wear barely any armour at that strength, a Cleric starts making mistakes, only the Thief can still do what it's good at with low scores across the board.
If you're starting at a higher level, or thinking about a tournament rather than campaign play, things change. Also, if you're taking non-core supplements, simply picking an overpowered race or class (especially in a front loaded game at low levels) will be easy, but I wouldn't consider that particularly sophisticate powergaming. The best kind is making use of the resources you have.