While I do play both single and multiplayer games, I prefer single player games and am honestly biased towards them.
Games that emphasize storyline or/and exploration really capture me and they capture me quite easily too. Notable games can include the Mass Effect series, games by Bethesda such as Fallout 3 and Skyrim, and other storyline driven games like the Uncharted series. If a single player game fails to excite me (such as Mirror's Edge or Star Wars: The Force Unleashed) then I won't make a return to playing it.
If a single player game has a multiplayer component, I may play it and I'll continue to play it if I actually enjoy it. However I'll only start playing multiplayer once I've finished the single player campaign. Notable games can include Mass Effect 3, Uncharted 3: Drake's Deception and Splinter Cell: Blacklist. I would include Mario Kart 8 for the Wii U on this list, but I have trouble playing online for some reason. Something to do with my connection?
I enjoy co-op games too and when it comes to co-op, I prefer split screen on the one television and console. Sadly there aren't a lot of games that offer that so much anymore, but a few examples here can include Diablo III for PS3, the New Super Mario Bros. for Wii U and Super Mario 3D World for Wii U too.