Okay so after watching the live stream last night of Starcraft 2, I have decided that I want to buy Starcraft 1 but I am concerned that it might not work on Windows 7. Just want to make sure before I go buy the battlechest

It works fine on Vista. And sometimes it complains about compatibility there. The best way to increase your chances of it working is to use your CD-Key to get it added onto your battle.net account, then download the diskless, online client. It works pretty well that way. 
 
It really should work fine on 7. I hardly doubt that it wouldn't work.

I bet is no, but you can email the blizzard tech guys and they would answer you.

 Every single thing I've tried on Windows 7 has run better than when I had XP or Vista.  I have no reason to believe this would be different.  If anyone could confirm, that would be great.  Otherwise, I'll be able to tell you in about 35 minutes (downloading the client from battle.net right now).
 
EDIT:@HolyCrapItsAdam: Starcraft is the first thing I've run that goes to shit on Win7.  It starts, but I get massive graphical glitches periodically, making things unplayable.  Could be my video card (Radeon 3870X2), but I dunno.  Was looking forward to playing it again, too.  Tried troubleshooting via Blizzard Support with no success.  Contacting them is my next step.

YESSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS
 
Gotta love win 7 haters... Yes it works fine anything that works on XP works on 7. I am currently playing it on Win 7 64 bit no problems.

"  Every single thing I've tried on Windows 7 has run better than when I had XP or Vista.  I have no reason to believe this would be different.  If anyone could confirm, that would be great.  Otherwise, I'll be able to tell you in about 35 minutes (downloading the client from battle.net right now).
 
EDIT:@HolyCrapItsAdam: Starcraft is the first thing I've run that goes to shit on Win7.  It starts, but I get massive graphical glitches periodically, making things unplayable.  Could be my video card (Radeon 3870X2), but I dunno.  Was looking forward to playing it again, too.  Tried troubleshooting via Blizzard Support with no success.  Contacting them is my next step. "

I can download and install it now, if you want.
 
Shouldn't take more than 10 minutes.
 
Edit: Mind you, I am on a Win7 x64, netbook, so if anyone is going to have graphical issues or something, I imagine it will be me.

Menu graphics are messed up for me but once ingame it's fine and that's what matters. (Win7 x64 with 8800gtx / 4gb ram)

Huh, well I might have to go out and buy it to try for myself. It's only 20 bucks so I can deal with that. Thanks for the input everybody

Runs fine in xp compatibility  mod.

I have 64bit Win7 and it runs fine except for the Blizzard logo, which looks like it came back from woodstock with its psychedelic colors.

I guess I'm just unlucky.

Works fine for me in Windows 7 64bit. No need for any compatibility settings, whatsoever. If I were you, I'd go straight to Battle.net, make an account, register your key, and download the client off there. It's an updated install with the latest version of the game.

" Okay so after watching the live stream last night of Starcraft 2, I have decided that I want to buy Starcraft 1 but I am concerned that it might not work on Windows 7. Just want to make sure before I go buy the battlechest "

"
all right i have signed up here just 4 this reply, actually I found this site looking 4 an answer to the same problem, i'll give u what worked 4 me, u have to go on compability mode and check all 5 boxes(Run in 256 color, Run in 640×480 screen resolution, Disable visual themes, Disable desktop composition, Disable display scaling on high DPI settings), also check run as administrador, and chose windows xp SP3 in compatibility mode, now 4 a really stupid thing,   right click on Desktop and select Screen Resolution (in Windows 7) orPersonalize (in Windows Vista). Leave the window opens  , go play! 
To me that made it, i got all that from here: 
http://www.mydigitallife.info/2009/12/04/workaround-to-play-starcraft-age-of-empires-and-diablo-in-windows-7-or-vista-fix-color-display-issues/     hope it works 4 u, if it does let me now... "

It's gimpy as hell, but it works. I had to make a batch file, kill windows explorer(!), launch the Starcraft exe, and when it closes, relaunch windows explorer.
 
Give it some google-fu, good luck.

I bought a new copy that has brood war in for 7$ and it runs perfectly and might i add...it still kicks ass. I don't have a huge nostalgia factor for it,but it's genueinly a good game. Sometimes units make stupid paths though.

After some fiddling, I got the disk version o work on Windows 7 32 bit. To get rid of the funky colors, I had to check everything in compatibility settins except compatibility mode, and, for some reason, it requires you to have the screen resolution settings open while you play. I'm downloading the online client now and it hopefully works better.