I'd recommend VirtualDub (
http://www.virtualdub.org/). It is free, tiny, comes without annoying installer and works pretty good if the segments are in fact avis and the frame rate, dimensions and codecs of the segments are the same.
Since virtualdub is a very powerful tool, it has tons of features which might confuse the newbie. Here's a short guide:
1. open the first segment
2. Click File > Append AVI segment to append the other segments. If you tick the box a the bottom of the dialog window, VirtualDub tries to automatically append all other segments it can find.
3. Click Video > Direct stream copy
4. Click File > Save as AVI
If that worked, no re-encoding was necessary and the original quality of the video has been preserved.