For me, my best weapon is the alien blaster. I made a gunslinger build because you pretty much have to if you want to use it. It's just so damn strong - with 10 agility, you get about 10 hits in vats, while hip firing outside of vats is as small a target range as you can get, even with a long barrel if you put points in the steady aim perk. With a scope and long barrel, it's as good as any short range sniper, with 300+ range. Furthermore, this gun is considered silent, so it can be used for sneaking, but it doesn't benefit from that silent weapons perk. It's practical in pretty much every situation, the only downfall of this weapon is it's rather slow projectile speed, about as slow as the old Fallout 3 plasma rifles.
My favorite weapon is either the alien blaster or the gauss rifle. The gauss rifle, like the alien blaster, just has that cool factor that's hard to not like. I really like that it can be charged, but doesn't have to be, giving you some choice in your snipes. The gauss rifle, also, while not practical for it because of it's slow-ish rate of fire, is usable hip-firing in a bind when enemies get too close because of it's small hip-firing target.
Late game, if you have the perk points in gunslinger and rifleman, with these 2 weapons, you have every situation possible covered with the best gear you can get for the job.
Well that's mine, what's yours?