So, I was wondering if anyone knows if a person who has a retail version of a game can go online and play with someone who has the steam version of a game, or if there will be problems. Thank you.

You can play together just fine.

Indeed you can. If a game uses Steamworks for matchmaking, you'll be required to activate both copies anyway, and if it doesn't, the game's own servers likely won't even be able to tell which version you play. Played Borderlands just fine between Steam and non-Steam version a few hours ago. ^_^

Excellent, thank you.