Buying it on Steam isn't a bad idea.
There's a good community that sprang up around it, and you'll get Steam multiplayer along with some slightly better graphics.
They also actively update AOE2:HD based on requests from players with things you won't get from the CD.
If you want to run what you have without a CD, I would recommend downloading the unofficial/soon-to-be-official expansion Age of Forgotten Empires It includes a color fix for Windows 7 and removes the need for a CD.
gaming.stackexchange.com/users/43782/Son of a Sailor
In most places it is legal to make copies of software for personal use so long as only one copy is run at one time.
I am not a lawyer and this isn't legal advice, but I believe this is true in the United States, Canada, and Europe so long as the CD doesn't have any copy protection.
Therefore, for personal use, in such places you can legally make a binary image file of the disc (an "ISO") and then use virtual drive software to load the image so that it appears to be a CD drive with the disc in it.
I've done this personally with my very played copy of Oblivion since I started to get concerned about disc damage.
I won't recommend any particular software because it depends so much on your exact OS and sometimes on you disc drive, but any CD cloner and any virtual CD drive software will do the job.
gaming.stackexchange.com/users/4163/SevenSidedDie
Back in the days when I played it with friends in my LAN
I made an image from the CD and mounted it with daemon tools.
Worked fine.
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This might not have to do with your question, but if by multiple computers you mean playing with people connected to a private network at home then this will be useful.
When I play with 5 or 6 people at home and 2 discs are required, we have to take the cd out of the host computer and put it in someone else's, wait for the "cd" to appear by that person's name, then put the disc back in the host computer and start the game quickly.
We have 2 discs but we always lose one
so this method always comes in handy.
gaming.stackexchange.com/users/57838/user57838
Try to install the DLC mod: The forgotten Empires.
Its installer can also launch the game, and it works fine without the disk and also as the main launcher for the game.
You can get it from here: http://www.forgottenempires.net/aof
I installed the game but couldnt run it, because the oficiall launchers were giving me errors, but that solved my problem (and also the problem of the disk)
Just make sure to paste and leave it on the main game folder before and after installing it, then create a shorcut and move it to where you want.
gaming.stackexchange.com/users/158097/ALG
I can't seem to find anything online that would suggest I can play this game legally without a CD. Not to mention, the CD I own has a chunk of it missing (it still plays fine and installs fine), and having it on multiple computers is a hassle because of the CD always needed requirement.    Is there any way to do this? Whenever I try playing without a CD, I get this:
Is there any way to play AOE2 without a CD legally?
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<age-of-empires-ii-the-age-of-kings>
gaming.stackexchange.com/questions/128054
gaming.stackexchange.com/users/18916/korrasaur
You can buy it on Steam or make a copy of the software for personal use. There are plenty of ways, in order to play AOE2 without a CD, legally, such as buying it digitally.
Few methods, that can help, are suggested.