Any text editor will do this, as long as the files are properly made XML files.
Which, if they are kosher GPX files, they will be.
I've used a text editor
1 to stitch GPX files together on multiple occasions - it's relatively easy providing you know which bits to delete and which to leave alone. Recalculating the timestamps is a bit more involved, however. All that said, if you're dealing with very large fragments, the potential for screwups is greatly increased.
I'd not be surprised if at least one of the online route planners allows you to import multiple GPX files, mash them together and re-export them as a single file.
Nowadays, I use a Mac app of my own design to do various interesting things to GPX files (split, merge, general mucking about with) prior to uploading them into my iOS GPS apps, but unfortunately it's nowhere near ready for the big time
2 (which is to say it's entirely command-line driven and has no user-interface to speak of)
1 - vim.
http://www.vim.org/2 - which is not to say I'm not prepared to distribute it at all, but it would take someone terminally brave and/or foolish to use it in its current form (unless they're me)