Wrex and Ashley. Wrex cause he's badass, and Ashley cause I want to bang her. Sent Kaiden to his death because of the latter reason. I love this game. 

I wanted to save Ashley but for some reason I fucked up and wound up with Kaiden. I do remember being pretty bombed the night I finished ME though.

Ashley and Tali. Tali for her hacking and decryption, and Ashley for gunner support. Played mainly biotic characters.

Also I never got to fuck anyone is ME. Did I do something wrong?

 Mass effect is one of my favorite games of all time, and a lot of it has to do with the great characters and dialogue. 
so when i was choosing my party members i would usually choose based on who i would want to have when talking to an npc or  who i liked the most as a character.
rather than choosing the character who would have complimented my character in combat. unless i knew that there was a really hard fight up ahead i would think of combat second. i still need to play through a second time, so maybe ill try it the other way around this time.
who else chose characters like this?  or was it just about whose powers/skills you liked the most?   
 
(i guess my internet is being really weird.) 

It depends. Tali and Wrex for the most part, but I usually had Tali switching out with Garrus depending on who I wanted to come with me.
 
Used the others a small bit, but not as much. Tali + Wrex worked fine for me. Though Garrus was a beast with a super-powered sniper.

" Also I never got to fuck anyone is ME. Did I do something wrong? "

I would usually change things up, always making sure I had at least one character with decryption skills. Although near the end of the game I decided to go with Liara + Ashley and I do regret it.

Garrus looks really cool, and Tali = no explanation necessary. 

Garrus because thats basically me in videogame form. And....i mixed that other slot around some.

It depended on who my main was. With my soldier, Tali and Wrex. 
 
When I played with an Infiltrator I rolled with Ashley and Liara. 

Wrex and Garrus.  They initially have some beef with each other (with the Turians making the Krogan infertile), so I brought them along just to hear them banter at each other.  Then I noticed that Garrus is a killer with the sniper and Wrex is a monster when you give him a shotgun and let him run around.

Totally fucked Ashley in my first playthrough.  I'm on my third playthrough this time with Garrus and Wrex to clean up some achievements and to familiarize myself with the universe again before the sequel comes.  Anyways, I chose them because I decided to be an Engineer this time around and shooting just isn't my game unlike my first character, where I played as a Soldier and easily trounced any opposition in the game with Ashley and Wrex backing me up.  Not that it matters in this thread, playing any class other than the Soldier actually made the game challenging and more enjoyable.

Wrex and Garrus; because they had the two best interactions, and I absolutely despised the rest of my crew.
 
Those two were awesome though.

 kaiden and wrex i just think they have the best back stories I mean ones whole
species were made steril and the other was  experimented on like a lab rat