What are the strengths of each of the Eevee evolutions? For example, which of them have the best speed, or highest defense.
The base stats of the eeveelutions are spread as follows:
Eeveelution HP Atk Def SpA SpD Spd Vaporeon 130 65 60 110 95 65 Jolteon 65 65 60 110 95 130 Flareon 65 130 60 95 110 65 Espeon 65 65 60 130 95 110 Umbreon 95 65 110 60 130 65 Leafeon 65 110 130 60 65 95 Glaceon 65 60 110 130 95 65 Sylveon 95 65 65 110 130 60
As you can see from the above,
- Vaporeon has the highest HP stat;
- Flareon has the highest Attack stat;
- Leafeon has the highest Defense stat;
- Espeon and Glaceon have the highest Special Attack stat;
- Umbreon and Sylveon have the highest Special Defense stat;
- Jolteon has the highest Speed stat.
All the Eeveelutions have a base stat total of 525, although that is spread onto different stats as Jerry points out in his answer, therefore 'Best' is not a term I would use when describing the various Eeveelutions. Each has different strengths and weaknesses - different Abilities and movesets and (obviously) different typing that allow any of them to fill different roles at will.
There are currently 8 Eeveelutions: (Bulbapedia)
In terms of competitive play, Smogon has some good analyses for Black/White, and is slowly getting there with X/Y builds & movesets.
You can find the Black/White analyses here, although do note that some of these are slightly out of date:
Here's the current Sylveon thread as well, although note that nothing has been finalised as of yet.
However the ones I've used & found most useful are:
Although the nerf to Rain in Pokemon X/Y hampers strategies involving the Hydration Ability (status heal under rain, works great coupled with Rest), Vaporeon still makes a splash as a Tank/Healer with it's High HP & Defense and access to Wish (Egg move) and Protect. It also has a decent movepool to choose from including Surf and Hydro Pump, although I've had great success with Scald (gotta love that 30% Burn chance) and Ice Beam. Water Absorb is still a viable Ability, and works well as a switch-in to an enemy Surf/Hydro Pump, on in a Team environment.
Slow but powerful in Special Attack. Unfortunately Ice isn't the best typing defensively, It only resists itself and is weak to Fire, Fighting, Rock and Steel, which are common on many teams. Blizzard or Ice beam are a given, with Signal Beam or Shadow ball for coverage. The other two moves I'm currently running with are Wish and Protect. Wish is probably not the best move on Glaceon, simply becase it doesn't have the Speed or defense to pull it off, but Protect has worked fairly well.
Great Speed and Special attack, and OK Special Defense, but not much Physical Defense to speak of. It's ability Volt Absorb allows it to switch into enemy Electric moves like Thunder, absorbing them as health. I'm using Thunderbolt, Signal Beam, Volt Switch and Substitute, although I've found that I rarely use Substitute. Going off of the Smogon page for Black/White, a possible replacement would be Hidden Power Ice
The rest I haven't used, although like I mentioned earlier you can check out Smogon's Black/White pages for suggestions, although remember that they are for Black/White currently