A program which grabs files, throws them together and renames them

[Davy Jones]

In this case, I downloaded zip with many many folders and subfolders, but in each folder are just a few files. No big deal, I could throw them together, but they share identical file names:

- folder 1: sample0, sample1, sample2, sample3...
- folder 2: sample0, sample1, sample2, sample3...
- folder 3: sample0, sample1, sample2, sample3...

So I have to rename each file and this gets annoying.

Is there a program which solves this? I mean, it should grab every file from these folders, put it in just ONE folder and rename everything.