This is probably not the best place for your question, but anyway...
Do you need a home video editing solution, or a professional tool?
Some may argue whether FCP is truly professional, but anyway it is used as such by many editors. (the latest version X is not quite ready yet for Pro use, but probably will be eventually)
On Linux, there is nothing comparable. At least for now. My main machine is Linux, and I did have a look at a few things like Cinelerra, Kino, Blender, etc. Some of these programs may be good for some specialized task, but none is a serious general purpose video editor.
In Windows, you have the really professional Avid systems. The learning curve may be steeper than with Final Cut, but if you envision editing as a profession, you will need to know it anyway.
The semi-professional alternative would be Adobe Premiere Pro. Here, some may argue that it actually is professional - and it is sometimes used for ads or for some TV programs - but I never heard of feature length movie released in theaters and editied on Premiere. But depending on your needs, it may work well for you.
Finally, for home video editing, there are several other Windows programs (Vegas, etc).
I usually recommend Final Cut Pro, even for people who don't have a Mac and will need to buy one. FCP is relatively easy to begin with, but can still scale to bigger projects. If you don't need the professional features which are missing from the latest FCP X, consider getting that.