I was able to install both Starcraft and the expansion, Starcraft Broodwar in Windows 7 x64. But when I tried to install the 1.14 (bw-114.exe) update it fails. The work around for me was to install Starcraft and Broodwar on Windows 7, then take a good install in a pre-Windows 7 install and copy (overlay) the files (already upgraded to build 1.14) over the installed files in (example) C:\Program Files (x86)\Starcraft. This worked.
With Nvidia GTS 250 (latest reference drivers as of 4/6/10) there were some graphic issues in the cut scenes, but the game worked just fine.