I'm surprised you can't do this with VirtualDub - I'll take a look later.
I have an old version of Premiere Elements which can certainly do this, but is probably overkill for what you need - e.g. it supports lots of transitions. It's also a tad slow and re-encodes video when it shouldn't need to - some video editors can repackage video data without fully decoding then re-encoding it in some cases, speeding things up dramatically.
You could take a look here : http://www.osalt.com/premiere#alts
And particularly at Kino : http://www.kinodv.org/
I've not used it, I'm afraid. It's most likely overkill for what you need, but odds are it won't be too hard to find just the features you need.
Personally, I use an ad-hoc mix of tools for doing jobs like those you describe. I use a truly ancient version of TMPeg DVD Author for most basic editing. This only accepts DVD-ready MPEG 2 and VOB files (which means it's fast - it doesn't decode-then-re-encode).
When I don't want the output as a DVD, I use Join VOB Files to, well, join the VOB files for a particular video where it exceeds 1GB, and I use the ffmpeg command-line utility for recoding.
ffmpeg is supposed to be able to join multiple files, including VOB files, but I've always got corrupt files as a result. JoinVOBFiles gives less corrupt files - timecode issues that get fixed when the output gets re-encoded.
ffmpeg can also cut sections out of a video file, but there's no GUI for selecting the ranges you want.
TMPegEnc DVD Author and JoinVOBFiles both work so fast that the limiting factor is hard-disk speed. They work much faster if the input videos are on a different physical hard drive to the output, so that there's no "thrashing" of the hard disk heads.
ffmpeg is scary - lots of options, many hard to decipher - but it's not too difficult to handle the basics. When you get something to work, keep notes so you don't have to figure it out again and it's fine. I usually end up with something like...
ffmpeg -i inputfile.xxx -acodec libmp3lame -vcodec libxvid -qscale 8 outputfile.avi
Nero has included a video editor which is technically more powerful and flexible than TMPeg DVD Author for some time, but (1) it's tricky to convince it to do that no-re-encoding optimisation, and (2) the user-interface doesn't quite work as well for me - controls are too fiddly etc.
TMPegEnc DVD Author may itself be far more powerful these days - I bought it nearly 10 years ago.
That's a confusing mix, and I would rather have a single-program solution that works as well and as quickly as my usual three-programs mix, but I stopped spending time on it quite a few years back.
If I need sophisticated, I have Premiere Elements. Mostly, the time saved by the fiddly-mix thing with DVD Author etc outweighs the annoyances. Nero is technically somewhere in the middle, and somehow manages to never be the right solution for me, though it's probably easier for a lot of people than what I do if you don't mind it being a bit slow and the UI being a bit fiddly.
Oh - Windows XP included a "Movie Maker", and Windows 7 includes a "DVD Maker". I've not tried either, but my guess is that they're on a similar level to the Nero approach. When I bought DVD Author, I was still using Windows 98 and 2000 - XP wasn't released until 2003 IIRC.