You could view it as a feature: since each directory is named by the CD label, you can easily write configuration files that mount the correct game directory, that way you can make sure the right CD is inserted.

If you don't want that, you will have to change your media notifcations. I'm not terribly experienced with them (I rather like the default behaviour), but the software package involved is called "hal" or "hald", perhaps that helps in tracking down some useful documentation.

Hmm, wonder if it's because I upgraded from edgy...
It is always this for me...

/media/cdrom0

How about
/cdrom

?

You could view it as a feature

You're right... I should make the most of it. It is quite handy. It just means that if I want to change directory to the cdrom, I have to know a) which cd is in the drive, and b) what the manufacturers called it!

I'll have a look into hal, thanks for the info.

Hmm, wonder if it's because I upgraded from edgy...

Don't think it can be, I upgraded from Edgy too...

Not sure if this will help, or is precisely what you're looking for, but I managed to find something for openSUSE to change that behavior. Don't know how well or how much would need to be changed for Ubuntu.
It's at http://en.opensuse.org/SDB%3AMounting_to_Static_Mount_Points

That looks ideal, but the problem seems to have fixed itself. I'm quite confused. I added these lines to fstab:

1/dev/scd0   /media/dvdrecorder   udf,iso9660 user,noauto     0       0
2/dev/scd1   /media/cdrecorder    udf,iso9660 user,noauto     0       0 

Expecting that I would have to manually pumount the disc and explicitly mount them this way, but now it just does it. Which is cool. And if I want the old behaviour back, I guess I can just remove them. Tada!