Can someone share with me a list of games that allow you to play as humans who fight aliens invading Earth?

The bestest one EVAAAAAAARRRR is obviously X-COM.
Then you have things like Crysis, The War of The Worlds (RTS from 98!), Half-Life2, Duke Nukem 3D and that's all that came to my mind.

Area 51 and it's sequel, Blacksite: Area 51
Prey - does this count since you are abducted onto their ship?
Anomaly: Warzone Earth
The Conduit
Crysis and Crysis 2
Serious Sam series

Space Invaders. :)

I must admit that this is a pretty broad topic to me. Like if I asked for a list of games with zombies in them.

Chicken Invaders

Probably get laughed off the forum for this but you could try the independence day game otherwise knows as id4.

From the GOG catalog(ue):

Alien Shooter: http://www.gog.com/gamecard/alien_shooter_expansions

Alien Shooter 2: http://www.gog.com/gamecard/alien_shooter_2_reloaded

Alien Breed: http://www.gog.com/gamecard/alien_breed_tower_assault

Action games with an alien theme, though for the most part you could substitute "alien" with "generic monster" and get the same games.

Then there's Destroy All Humans! for a reversal when you get sick of defending us filthy humans. Don't know if they ever ported it to PC, though.

How do you know humans are weirder than aliens unless you have met aliens?

Because the only thing really weirder than a human is a platypus. They have a 4 headed penis, that's very weird (and disturbing, don't google it, you've been warned).