I recently signed up with ComputingHost.com because the price and offers are fair. However, the most important feature I needed was free add-on domains as offered by GoDaddy.com (if they still offer it) In the end, ComputingHost required me to purchase another domain.

So what I'm looking for is a web hosting (not free) company that offers free add-on domains (doesn't mean unlimited) Is there any out there I might not have found yet?

I can't seem to find that piece information on GoDaddy right now, but I think you've misunderstood what they were offering. If it said "Free AddOn Domains", it probably meant that adding one was free. However, you would still have to be the owner of the domain you want to add, which means you would have to pay for it.

Most hosts do offer free AddOn domains, but some require additional payments, that can cost even more than a domain - that's probably why this option was stated at GoDaddy. Of course, I could be wrong, but why would anyone be giving away 10 dollars?

http://www.foreverhost.us/personal.html

Check the above, and check it carefully. It sounds to good to be true, right?
It's an actually, reliable and trustworthy host. I've been there for a year, hosting expired, and in need of a free host. Which is why I'm here.

Make sure you know the difference between a subdomain and an addon domain. Sub domains are often offered free of charge.

To sum it up, you get unlimited SUB-domains, ftp accounts, email accounts, space, bandwith (the space just starts with a few gigs. One you're going over the limit, they'll just extend it, to no cost), fantastico, myPHP, the whole sweet deal. I took the 8.99 dollar plan for a year, and also gave them the money to get me a domain name. They did at GoDaddy. All in all, I think I paid about 20ish dollar for the entire year and got dreamhosting. I've seriously NEVER had any downtime. Support can be a little slow, but given all the advantages...
The 20dollar deal a year gives you 4 extra addon domains
I had about 3 full, running websites, ran about 4 heavily visited fora, had a few picture galleries, etc.

Reason why I'm with astahost is that they offer almost the exact same sweet package without the subdomains, which I don't really need.

Wow! Foreverhost.us sounds too good to be true! If I sign up for a lifetime package, do I get add-on domains?