If you run Windows you probably have Microsoft Movie Maker. Or it's available for free download from Microsoft if your PC didn't come with it installed. Like most MS applications, it's very user friendly to the point of being idiot-proof, but like most MS products it's prone to weird and unexplained errors
- like if you apply slow-motion to one clip, the next clip inherits that with no way to turn it off.
- sometimes the project your working on will "freeze" and of course the only way out is Ctrl+Alt+Del to kill the program. Make sure your auto-save is set to save your file like every 10 minutes.
- sometimes a clip will freeze like you had inserted a still image. sound still works, but the clip is wrecked usually can't be fixed.
- sometimes when overlaying audio it loops a segment of the track rather than the whole track. I think this might be related to some DRM protection though and not necessarily Microsoft Movie Maker
In fairness most of these things happen very infrequently, but of course they always seem to happen at the most inopportune time or when you have put a lot of work in to a project.
The pros: it's free, and easy to use.
The cons: prone to funky errors that you can't fix, doesn't have a ton of features
Overall it's a good enough product to get started and get a feel for putting songs & splicing video clips together with some basic transitions, effects, etc.
I recently got Corel Visual Studio Pro but have really only used it a few times. A guy I know uses Final Cut Express which can make some nice clips. Both of these are better applications, there's a bit of a learning curve (they don't work exactly like MS MovieMaker but this can be a good thing) and they have more effects and features available.
I think Final Cut might be a Mac application. Also for macs there's iMovie, but I don't have a mac so I can't really speak to either of these.