If the game requires Steam you must install Steam in order to use it, and you must be logged into the Steam account associated with the game's key (the code you got in the box/on the manual/etc) in order to play it. All Valve titles, including Portal and Portal 2 require Steam, as does Skyrim, Civilization V, and many other games. The key that comes with the game discs is only allowed to be activated and attached to a single account, and cannot be transfered once used.
This may be confusing if you're thinking in terms of discs - up to this point we've been mostly trained to associate "disc" with "game" - but that's not the way it works with Steam. You may as well throw the discs out when you buy a boxed copy and just keep the key (not literally! just employing hyperbole ;) - the discs are next to useless for most of these games. In some cases, Steam will just download it from the internet, even if the disc is present in the drive!
That having been said, if you're not interested in the online components of Steam for a given game (ie, Portal 2's co-op mode, and certain game achievements), it is possible to play multiple games -including multiple copies of the same game - from a single account on multiple computers at once. You'll have to put Steam into "offline mode" on all but one of the machines you plan to play on.
Offline mode is described in the Steam Support Docs:
- Start Steam online - make sure the Remember my password box on the login window is checked
- Verify that all game files are completely updated - you can see the update status for a game under the Library section (when the game shows as 100% - Ready it is ready to be played in Offline Mode)
- Launch the game you would like to play offline to verify that there are no further updates to download - shut down the game and return to Steam once you have confirmed that the game can be played
- Go to Steam > Settings to ensure the Don't save account credentials on this computer option is not selected
- From the main Steam window, go to the Steam menu and select Go Offline
- Click Restart in Offline Mode to restart Steam in Offline Mode