It depends on the website. If I got one on here, then yes! Or another forum or a gaming website; yes! But if I got a random friend request on Facebook, then no, because I keep that for only personal use, and mainly family & friends I've met IRL.
I don't usually send friend requests, I can't even remember the last time I did! But if I was to, then it would probably be to someone I could relate to or whatever.