I'm playing Portal 2 (Windows XP version), in chapter 5. When I try to save, the game tells me there are no saved-game slots left, and I will have to delete some saved games. I find this behavior incredibly irritating. Is there some way I can get more room for saved games?
I don't think you can do what you ask, but unless you want to keep saves to access extremely specific parts of levels, you really don't need any more saves. Once you've finished a level you can always go back to it afterwards and play it again. So if there are some puzzles you like, you can skip straight to them (or to the beginning of the chapter, anyway).
Addendum from comments: Remember, you can always quicksave (F5) and quickload (F9), which is much faster. But you always overwrite your previous quicksave, so be aware of that. However, due to the design of the game it's essentially impossible to lose any progress short of a complete wipe of your saves.
If you are on Windows, go to this directory:
C:\Program Files (x86)\Steam\SteamApps\common\Portal 2\portal2\SAVE.
There should be another folder in there. Go into that and you can copy your saves to somewhere else and remove the ones from this folder. Then you will be able to save as much as you want in-game, and you can keep the saves you want for future use.