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
Presumably your copy has some method of circumventing Steamworks that persists even when you attempt to download changed files from Steam. Backup your saves (located in "C:\Users\Your Username\Documents\My Games\Borderlands\SaveData" for Windows 7/Vista and somewhere similar for XP) and remove Borderlands entirely. Ignore step one and step three, simply let Steam install the game. This should restore full Steam compatibility.
Best Answer
The games you buy are yours forever (or rather a very long time) and can be installed on as many computers as you want (unless the game has a limit on its own, but the same limitation would likely be on the physical edition too).
Dumping physical copies is a decision you must make, but as I stated below, Steam has been around for 13 years already, and they are likely to be around for a very long time. I don't like physical copies as buying, storing, moving and organizing them is hard yet losing them is pretty easy.
Steam is generating billions of dollars every year and is unlikely to go bankrupt, and even if it did, most developers would provide a way to move your games to another platform, like most developers did when Desura went bankrupt.