The Mass Effect cast actually produces a lot of winners here, because damn near every single one of them has 2 great best friend factors: a)they're smart or interesting or loyal or attractive or combinations of two or more of those and b)they ain't nothing to fuck with when the fighting starts. With that said,
Garrus because despite the aforementioned goodie-two-shoes-ness he was always one of my favorite team members in terms of both personality and fighting style and he's also (especially since ME2) a reasonable and loyal dude who will consider what you have to say if you have a forceful or magnetic personality. And because he's unstoppable in a fight.
Mordin because he's direct and hyperintelligent so you'd always have an advice man, and he's also relatively morally ambiguous so you could always trust him to give you a relatively unbiased opinion of a situation if you asked it of him. Again, not one to fuck with in a fight and as a bonus, if you got virtually any disease he'd probably whip up a cure for you before you even started showing severe symptoms.
Liara because I did say some of them were attractive, now didn't I? Also intelligent applies here, and yet again she was my other favorite team member in the original, total biotic powerhouse. Don't tell me it wouldn't be fun to have a friend who can bend space-time at will.
And finally... Jehuty (Zone of the Enders). Technically you can't make friends with the Frames but you can befriend and directly influence the personality of their AIs through your actions, and having ADA as a best friend would mean you could fly motherfucking Jehuty which as far as I'm concerned was always the coolest of all those mechs, even with Anubis in the picture. Being a skilled runner and flying Jehuty would basically confer the same status upon you that Tony Stark has in Iron Man except you'd be a way more effective enforcer of world peace because you could probably circle the globe in a matter of minutes at maximum speed and the world's entire military arsenal, nukes included, wouldn't be nearly sufficient to stop you. Alternately if it floats your boat, Jehuty/ADA is a perfect companion for the world dominator/destroyer for exactly the reasons listed above.
