Is it possible to play two different Steam games on the same account at the same time?
Solution 1:
As far as I know, you can't do that. If one of you wanted to play single player, then you could possibly set one computer to Offline Mode before starting the game, and then the other person should be able to log in on the other account and play multiplayer, but both of you being online at the same time should not be possible.
Keep in mind, this is technically not allowed. Steam's agreement says you're not allowed to share your account or your games, that includes your fiancee. I don't think they actually do anything about it as long as you're not talking about it on steam chat or their forums. However, you still risk losing your account and all your games when bypassing their rules.
EDIT: As of mid 2014, Steam has released Steam Family Sharing, which enables the sharing of Steam libraries. However, this system does not work on a per-title basis (only during the beta), but rather - If one title is being played, all other titles cannot be played (unless it's the same user that's using the library that is launching the second/whatever-is-after-first program).
Solution 2:
This is technically against the Steam terms of service. You have not purchased the game, you have purchased a license to play the game. It's buried in that legalize and the difference is subtle but important. You have permission to play the games on your account but your fiance does not. You have permission to take your games anywhere but you can only play them on one machine at a time. Steam works on an individual basis not a "friends and family" basis, so only one person can play that game at a time, and technically it should be you. If your fiance wants to play a game she needs to purchase a license to play the game on her own account.
The steam TOS is located here, http://store.steampowered.com/subscriber_agreement/
Valve hereby grants, and you accept, a limited, terminable, non-exclusive license and right to use the Steam Software for your personal use in accordance with this Agreement and the Subscription Terms. The Steam Software is licensed, not sold. Your license confers no title or ownership in the Steam Software.
Solution 3:
Steam just recently (October 2013) released an update that allows something called Family Sharing. Two Steam accounts can now share games with each other.
Solution 4:
I believe you can. If you log into an account, then go into 'off-line mode' you can log in somewhere else. You may have to disconnect the first machine from the network/internet before logging in again.
Solution 5:
No, there's not way that I know of to accomplish this.
See this related question in which I have the same problem, I found no way around this limitation.