In the Pokémon games — especially the early ones — an Eevee is a rare gift. These Pokémon don't seem to be found in the wild, and are given to you by Bill or some other special event. What's awesome about Eevee is that it offers a bunch of evolution episodes. Gen one offered us three, gen two offered us two more, and the cycle just kept going. The Eeveelutions are awesome and every trainer has their favorite, so it can be tempting to evolve your Eevee right away into something awesome — but maybe you should wait?
Well, there are reasons to do either, and it all depends on what kind of trainer you are and what you want to get out of this.
10 Evolve: Type Advantages
The obvious reason to evolve your Eevee right away is for a quick type advantage. Let's be honest — the normal Pokémon isn't great against much. It's solidly average because although few types can be super effective against it, it's super effective against even fewer. Evolving your Eevee into a much more dynamic type will give you a type advantage in so many battles, and who doesn't want to have those ASAP?
9 Wait: Happiness Evolution
If you want a happiness evolution from Eevee, you'll have to wait. In many of the games, Umbreon and Espeon can only be achieved when your Eevee is super happy and bonded to you. It might be tempting to use a stone to get a quicker evolution but if you want one of these types, it really is worth it to be patient. Take your Eevee for a haircut, give them lots of treats, treat them well — they'll be your Umbreon or Espeon in no time. Just make sure to stop the evolution until the appropriate time (day for Espeon, night for Umbreon).
8 Evolve: Better Moves Quicker
If you evolve Eevee fast, they'll learn better moves quicker. For example, if Jolteon learns a specific electric move at level 30 and you evolve Eevee at level 35, they've missed it. If you plan to load your Eeveelution up with moves specific to their type, then it might be a good idea to evolve as quick as you can.
7 Wait: Moves Exclusive To Eevee
If you do want your Eevee to have a few moves that are normal, you might want to wait. Eevee learns certain moves at certain levels that just won't happen if you evolve them too soon — as is the same for any Pokémon who can be evolved with a stone! It might be worth looking up which moves Eevee is going to learn and deciding then if it's worth waiting any.
6 Evolve: Raised Stats
The obvious — if you evolve quicker, there will be raised stats. Umbreon in particular tends to have awesome defense, so if you're looking for a good Pokémon that can take a bunch of attacks before fainting, it's a good way to stall a battle! But all of the evolutions have raised stats, so this is just an advantage all round.
5 Wait: Make Sure You're Certain
There are so many Eeveelutions now. Even when we started off with three, it was a lot of choice — but with every generation, they give us more.
It might be worth waiting to make sure the Eeveelution is the one you want. Sure, some of them are cute and you might want to rush into it, but in many of the games you only get one Eeevee.
(Of course, if you're playing Pokémon Go, have at it, because you'll get plenty of chances. No point in waiting there!)
4 Evolve: One Less Pokémon To Worry About Leveling Up... Sort Of
When we have an evolution coming up, we tend to get hyper focused on that Pokémon which can dilute your attention from the party. Once your Eevee has evolved, you're free again to divide your time equally. It's a small reason, but it might make the world of difference if you really can't decide whether to evolve your Eevee or wait.
3 Wait: You Might Find Out More About The Game As You Progress...
Maybe you should wait, because you'll find out more about the games as you progress. For example, you might come up against a gym leader when you need an extremely strong fire Pokémon and don't have one — hello, Flareon! But oh, wait. If you caved and evolved your Eevee into a Vaporeon earlier in a spur of the moment decision, then your chance at a powerful fire Pokémon is gone.
For tactical players, this is probably the best option and you should definitely wait and scope out the gym leaders and challenges the game will present. This is the smart trainer's way to play!
2 Evolve: Certain TMs Can Be Taught
You might want to evolve sooner so that you can use TMs on your Pokémon! Eevee can, of course, learn TM moves too, but not many. If you evolve your Eevee soon, you'll be able to use the TMs of their type and scope out which moves would work best for them.
1 Wait: Enjoy Having An Eevee!
The most obvious reason and yet the one that most impatient people seem to miss — just enjoy having an Eevee! There's no deadline or cut-off time for your evolution. The game isn't going to say, "hey, wait, you waited too long — your Eevee now must stay an Eevee forever." You can always evolve it at any time so maybe for some time, you should just enjoy having an Eevee. They're pretty unique in the games, and you're never going to have one again.
Of course, if you're playing Pokémon: Let's Go Eevee! then you'll have no choice, because the game won't allow you to evolve your Eevee. Maybe that's best, though — letting someone else make the hard choice for you!