For me, I normally play on a Single Player mode, I'm not sure why, but playing by myself seems to be better for me to do than playing with friends online or playing with me offline, although I do happen to play 2-player offline.

Same for me I always do single player.

I usually play on Single player modes. I can't play games as good as I could when I play video games with other people. I can't concentrate. So whenever I play together with friends or family, I see to it that they would play something casual and not-so-hardcore games. I'd rather play alone if I'm playing a hardcore game.

I do not play often on-line.
Period.
I go to a friends house for that.
I just grab my extra Controller and we either go at it head to head or as co-op.
With fighting games we pass the controller back and fourth between rounds when we are on-line. Totally Messes a person up with the strategy mix up.
(Some do "Keep away" while others "get up in the others grill".)
Sometimes we do this with "F.P.S." games.
But rarely.
(I like to use pistols, shotguns, and sniper rifles. My partner favours full auto machine guns, and rocket propelled explosives.)
Most of the time I normally play a game for a full completion off-line.
I do not need to have the whole world knowing how much training it took to get good.
My friend has no such problems but, they do like how when we team-up, it can dominate the board for a few hours.
Loads of fun to be had but it is hard to find people that are loose with their "On-line Gamer I.D."
Guess it only works with people my age.
Good Luck.

Good Luck To All.
I'm done. Stick a fork in me.
Peace.

I pretty much only go for Single Mode. There really aren't any games, for me, that are fun when played online. Sure, there's Super Smash Bros Brawl (Which is fun online or offline), but then you get eight million different shooter games taking up the whole multiplayer genre, in which (In most cases) they're all repetitive, boring, and (mostly for consoles) you get 6 year old kids swearing at you. The only shooter I've played so far that isn't like that with multiplayer is Broderlands, though, since it's co-operative, rather than Player VS Player.

I mostly play single player but I sometimes play as 2 players.

Well, it depends on what game I am playing. If it is like Call of Duty or something, I usually like to play multiplayer. But, for most games, I enjoy playing single player.

I mostly play single player games, they are just more fun. And I like story's and character development in my games, so single player is for me. I also feel that multilayer is usually tacked on, games like call of duty where multilayer is the focus is fine by me, but when a single player game like Tomb raider has it, just feels tacked on, and really that game didn't need it.   

I prefer single player games, by a long shot. This day, multiplayer games are full of hackers and modders, 11 year-olds, lobbyists (game hosts who intentionally don't start games to torment people), people who don't like to lose so they place kickvotes on other people... The list is endless.

While playing online can be fun, I start to resent it.