It's just as likely that the problem is with the disk mounter as the download itself if things other than DMG files download and mount ok (from the date it looks like the OP isn't going to need any more help, so just going off of alex.roy's question). If torrents and software update work, then your network is basically ok, and neither of those result in disk images, so they would bypass the verification/mount step.
Downloading an application contained in a .zip instead of a DMG would be one way to test--if it downloads and runs, then that's a good sign that it's the .dmg mount process at issue. I'm also assuming here that if you download something with Firefox you have the same issue, or is that ok?
I once had this happen to me (failure to mount DMGs), but a reboot cleared it up. You could try booting from the OS install disc and checking your hard drive for errors using Disk Utility and repairing permissions, to see if either helps. Also try creating a new user account, and see if DMGs work there.
I'd normally suggest downloading and reinstalling the Combo updater for either 10.5.8 or 10.6.4 (depending on which OS you're running), on the off chance it would help, but that's not going to be easy if you can't mount DMGs.