I have a love/hate relationship with dual-booting Ubuntu with Windows. The first Ubuntu I installed was 9.04. I installed it along-side Windows XP back then. That first time was a sweet discovery of what one can do with dual-booting. Let me share my experiences with the modes suggested here.
Installing Ubuntu Inside Windows via Wubi. This is the best choice if what you want to do is get a feel of Ubuntu first. But Wubi only allows you a storage of 30Gb inside Windows. As a newbie to Ubuntu and Linux back then, I was used to seeing a graphical report of my disk usage in Windows. I never had that feedback at first with Ubuntu. There was a day when I could no longer log in to Ubuntu. After Googling about my problem, I found out that I might have exceeded my 30Gb Wubi storage capacity. Also, you can't use the full capability of your computer if you just run Ubuntu inside Windows. This last reason was the reason that made me decide to install Ubuntu directly to my hard disk.
Installing Ubuntu Alongside Windows with one HDD. This is very much okay since that you can easily switch between Ubuntu and Windows using only one computer. Gamers, users of softwares that have no satisfactory open source equivalent in Linux, and people who work with Windows in their offices do this. I used to do this, too. There was a time, though, that I messed up during installation of an upgrade (from 9.10 to 10.04). I could no longer access my Ubuntu files and I did not know a work-around back then so I ended up backing up my Windows files and re-installing both Windows and Ubuntu again since I did not want to end up not being able to use the other half of my hdd. That was indeed some learning experience, one which I would not recommend especially if you want to maintain a day job.
Installing Ubuntu in another hdd. That is why I totally agree with wolfo9999 in this one. Hardware does not come cheap but at least you will not be troubled with messing your entire work in the other disk just because of a bug or an error that cropped somewhere during installation.