What's a free web hosting service to show temporary beta versions of my Drupal websites online ?
You can serve em from your house and just use a service like dyndns to resolve a hostname to your IP address at home. This is what I usually do myself.
To top it off, dd-wrt, tomato and some of the other router firmwares out there support these dynamic dns services and will automatically update your account for you regularly to make sure your IP address is set in their service to what it should be.
I personally use WAMP since its so quick to setup. From there you could go many different directions. I have an account with http://www.dyndns.com to redirect to my home IP. I also use named based virtual hosting which is easy to setup if you take the time then I can use something like this for my clients http://projectname.something.getmyip.com which will redirect them to their project on my server.
If you want to try this, I can give you some pointers to setup the WAMP instance..
If you'd rather host it elsewhere, any major site is probably as good as any other. You could go with godaddy, 1and1.com, etc... and get a cheap shared account for a couple bucks a month.