What advantage do I get by evolving my Pokemon?
I know that if I postpone my Pokemon's evolution, I can learn certain moves earlier. For example, Mareep learns Thunder at level 55 while its fully evolved form, Ampharos, only gets it at level 79.
Obviously, Pokemon who change types by evolving get the benefits of their new type, but for everything else, why should I evolve early as opposed to waiting for good attacks?
I recommend Eevee's Pokédex's "compare this family" feature. Evolved forms can both gain _and_ lose the ability to learn certain attacks, as well as learning them at different levels. For example, in the Bulbasaur family, Bulbasaur can learn Seed Bomb while Ivysaur and Venusaur can't, whereas only Venusaur can learn Earthquake by TM. In most cases, you only want to delay evolution to let it learn attacks, or because the evolved form isn't cute enough.
The advantage gained is improved stats. The evolved form of a Pokemon has better stats than its earlier forms. However, when you evolve your Pokemon their stats are recalculated from level 1. So your fully evolved Pokemon will have the same stats at level 100 regardless of which level you evolve it at.
There are two disadvantages to evolving a Pokemon though. The first one is pretty minor, and is that a Pokemon takes longer to learn moves in an evolved form (as you noted in your question). The other disadvantage is fairly significant though, and only applies to Pokemon which evolve with an evolution stone. The majority of Pokemon which evolve using a stone won't learn any moves when evolved, so you don't want to evolve those Pokemon until they've learned all their possible moves. Evolving them earlier will really, really limit their usefulness.
An evolved Pokémon requires no more experience to level up than its its predecessor would at the same level. Source: Bulbapedia
@JonathanDrain I could have sworn it made a difference. Perhaps it was different in previous generations.
@Wipqozn I'm lost, you said that they would have the same stats at 1 as 100 when evolved. So... then whats the point of holding off on the evolution?
@Ender: In the newer versions there doesn't seem to be a reason to hold off anymore. The only exception would be for pokemon which evolve through a stone, which lose the ability to learn new moves via leveling.
@Wipqozn That stone thing isn't necessarily true, see the Eevee evolutions for example. Instead, their movesets change depending on the stone used