How many unique Pokemon are there in Pokemon GO?

When you assign a pokemon to a gym, that pokemon stays there until it is unseated; you won't be able to assign it to a different gym, or use it when attacking rival team gyms. As a result it may be useful to have several of the same pokemon just so you have spares you can use in attacks or to assign to multiple gyms.

In addition to the current Pokemon (145 at the time of the question: the original Pokedex of 151 minus Ditto, Articuno, Zapdos, Moltres, Mew and Mewtwo), there are other reasons to catch multiple of the same type:

Different Move Sets: with the different moves on each Pokemon of the same type you will run into some that will more effectively counter certain Pokemon. These moves only change when evolved but aren't guaranteed to.

Busy At Gyms: if you leave a Pokemon to defend a gym it is gone to you until it is kicked out. Here depending on movesets having a back up is a good idea. It may not be 100% necessary, depending on the CP and movesets of your other Pokemon

Candy: catching a Pokemon gives 3 candy of the base for a Pokemon I.e. Pidgey gives 3 Pidgey candy pidgeot also will give 3 Pidgey candies. Transferring a Pokemon to the professor will give 1 of base type.
It takes 1 candy to power up the CP and 12-50 to evolve.

The original 151 Pokemon are currently available as of release.

There technically is no point in keeping more than 1 Pokemon unless you are going to evolve them later.

While there are only 151 Pokémon currently available, it's important to know that each one can have a different moveset from others of the same species, which could be a very good reason to keep more than one of any given Pokémon.

You need more room for the following:

1. when you have a lot of pokemon, you don't wanna go clean your storage every single time you catch another one

2. your will definitely have pokemon of the same kind, because, for example, if you have 2 Vaporeons with good IVs and Hydropump you definitely will wanna use them un battles or send to defend gyms. Or if you send one to the gym, you would like to have a good water type mon on hand to kick ass fire or ground type.

3. you will have your collection pokemon, that are just to have every spice, your potentially good pokemon that you look forward to evolve and your badass pokemon squad that you send to gyms and battle

well, this will make sense only on higher lvls though

Wondercricket's answer covers most of the question so I'll just add this:

Catching more than 1 Pokemon of the same type will give candies of that Pokemon's type. Those candies can either be used to power up or evolve that Pokemon.