I played a lot of Borderlands 1 and 2 solo, same with Diablo 1, 2, and 3. When not solo, I was just playing with 1 or 2 friends. I'm not a big fan of playing with strangers.
Destiny is a bit different though. I mean, you can do the story missions and patrol stuff solo, but there's content specifically designed for groups. The weekly heroic strike has matchmaking, but not the weekly Nightfall strike. You can try to solo it, but you're going to have a lot of trouble. There's also no matchmaking for the 6 man raids, or 3 man Prison of Elders from the second expansion. If you want to get into the more serious PvP, Trials of Osiris, you have to have 2 friends to do it. Playing solo limits what content you can access in Destiny.