The question of whether or not you can play Steam games offline is a complicated one. The short answer to this question is no, but the long answer requires a bit more explanation. Steam does not have an option that will allow you to go offline and still be able to access your account (although some third-party software may offer this), so if you want to get achievements and trophies on any of the games you’ve purchased from Steam, then they need to be downloaded at least once while connected online.
There are a few hacks for some games that might enable them to work offline in certain circumstances, but these most likely won’t work for all games or all computers and it’s up for debate how ethical it is using such third-party software.
There is also the option of creating a Steam Offline Account, which does not require you to always be online and will work even when no internet connection is available (though some features like playing games or making in-game purchases won’t be accessible).
This account can only access game libraries that have been downloaded from your main account on any given computer, but it’s still an effective way to play offline. Steam has made recent strides towards improving their service for gamers who don’t want to stay connected at all times: they’ve now added the ability to start downloading games before connecting online so that they’ll sync up with your other devices without having to wait until you go live again. They are also working on adding more