There are other VM options as well--Xen is probably the best-known non-VMware. I'm not sure how well it works yet, but I don't believe that Windows is suported.
WINE is another option. It comes in assorted flavors--WINE, Cedega, and CrossOver Office. Choose the one that best fits your needs.
You didn't mention which Windows apps you want to run under Linux. I've run Office apps, and a few games directly under Linux using Cedega, but not all apps/games are supported.
The windoze app that comes most quickly (no pun) to mind is Quicken - a friend of mine went to a WINE site that lists each app and how it works under WINE and it got an "OK but still buggy and some features don't always work right" rating - by that I assume that you could start it up and do some basic stuff but it wouldn't be an equivalent experience to running it on windoze - I haven't tried it myself however. I'm sure things will only improve and I can't imagine that Quicken does anything too exotic under windoze - it's OS calls I would think would be pretty basic - although I guess it probably has some hooks in to IE, which might be an issue.