Lots of OSs have a handy ~/Downloads folder where all downloaded files automatically go to. This is much cleaner than say, piling them up on the Desktop or elsewhere. I generally move something out of ~/Downloads if I need it, leaving the rest to pile up. Thanks to the very helpful tmpreaper, I have it automatically deleting any file older than 5 days from ~/Downloads. Now it manages itself. You can do this easily with Debian-based OSs (sudo apt-get install tmpreaper) or Mac OS X (fink install tmpreaper). You can cron it using a little script in the right folder:
/etc/cron.daily/tmpreaper_downloads (Debian)
#!/bin/sh /usr/sbin/tmpreaper --all --protect .localized 5d /home/hans/Downloads
/etc/periodic/daily/900.tmpreaper_downloads (Mac OS X + Fink)
#!/bin/sh /sw/sbin/tmpreaper --all --protect .localized 5d /Users/hans/Downloads