Virtualization allows this basically.
If you're running Ubuntu (or I suppose Linux in general) look into virtualbox. It's able to integrate the guest OS very well into the host OS.
Anything else, look into VMware player, the free version of vmware. (or you can go for the paid version) It allows you to run an OS in a separate window, but I don't think it has the integration option of virtualbox.
Other options are Parallels, VirtualPC, and Xen.
Xen allows for true coexisting OSes, but only supports linux currently.
Virtualbox, VMware, and Parallels are the top three imo.
Virtualbox I find is the fastest and has the best integration, while VMware and Parallels are interesting because they implement rudimentary directx acceleration. I don't think parallels has a free version however, while vmware does. (though it takes a fair amount of configuration to get working)
VirtualPC isn't that great.
If running Linux, Wine may also be an option to run some Windows apps.
Edit:
Oh, I see, you want games?
Well, you could run Ubuntu within a virtual machine on windows (I believe the latest release, 7.10 Gutsy Gibbon, has specific support for this) but you'll lose out on a lot of the advantages of running a Linux system. Well, at least imo being forced to run the slow booting windows and using NTFS over the more advanced linux file systems is a major loss.
You could use VMWare to run games within linux (not sure if parallels will work as well) but performance is severely crippled compared to windows and it supports only a small subset of directx features. Would work for less intensive games though.
You could also check out Wine and Cedega. Wine has fairly good support, especially for more common games.
Cedega is a subscription service ($5 a month) for a version of wine specifically geared to run games. However, cedega split from wine years ago and lacks many of wine's advancements, so whereas once wine gets one game working with certain windows dlls then just about any game that uses those same dlls will work, cedega works on a case by case basis. Both wine and cedega have app databases to see if the game you're interested in will work.
Also note, if you're running an ati card you'll likely have to manually update the drivers to the latest version to get good performance/compatibility. You may or may not have to for nvidia 8 series cards, I'm not sure of their current support in ubuntu.
Gaming on high end, recent games is likely not a possiblity though. Cedega works on a popularity basis so only the most popular recent games are likely to work and I still doubt support is that great. Wine is hit and miss, but at least it's free.
In reality, the only way to accomplish what you want will probably be to run windows with a virtualized linux.