Below is a list of basic requirements for MyBB. You must have these requirements fulfilled before MyBB can work on your website.

A host with the following:
PHP version 4.3.11 or above
XML Extension
MySQL version 4.0 or above
FTP access (or another way to upload the MyBB software to your web server)

 

http://www.godaddy.com/

It isn't free, but it is inexpensive!

 

I dont think you will find a free one with all that.

 

If you are serious about websites either for personal or your business, don't go to free web hosting as they are usually not reliable and you may end up losing all your hard work. Free web hosts usually put advertisements on your websites and it could be annoying.

If you like to create websites (usually you will end up more than 1 website, I got more than 100 websites in about 6 months' time), go for multiple web hosting services where you could host all your websites in one account.

I would like to suggest following webhosting which I use, they are excellent.

Hostmonster http://www.hostmonster.com/track/ryukenden/

They offer hosting of "unlimited domains" and you will get massive webspace of 300000 MB (300 GB ). They only charge $5.95/month and they offer "a free Domain Name" and installing service called "Fantastico". By using Fantastico, you could create own forum, photo gallery, shopping cart (e-commerce),your own auction site and your own blogs within few seconds. They also offer "Free Website Builder" as well.
Visit the site to check details.

Hostmonster http://www.hostmonster.com/track/ryukenden/


More the list of BEST WEB HOSTING sites visit

http://webaite.com/

FREE AD-FREE HOSTING.

If you would like free ad-free hosting, try

http://www.webzonetalk.com/hosting.html

 

Free web hosting usually not reliable and it may DOWN,,DOWN,,DOWN,,So your vistor will not come back .All your hard work may be lost and Search Engines are NOT on friendly terms with free webhosting site.Free web hosting are also have a lot of annoying advertisement...
I use HostMonster..HostMonster offers the absolute best value for web hosting available today. They have the best combination of features, reliability, speed, and price, as well as the ability to consistently maintain the best customer service in the industry. They also allow you to host UNLIMITED domains and UNLIMITED subdomains with 1 account! They offer UNLIMITED email accounts, extremely generous storage(200G!!!) and bandwidth(2000G!!!) allowance, eCommerce capibility, free setup, free domain for life, tons of free scripts and bonuses, they accept Paypal, and offer a 30-day money back guarantee. They also support PHP, MySQL, Perl, Ruby, SSL and more!

HostMonster offers tons of additional useful web applications such as 100 free MySQL databases, spam protection, web templates, Agora Shopping Cart, OS Commerce, Fantastico script library, Form mail, Guestbook, Bulletin Board, PHP Nuke, Chat, Blogger, Promotion Tools, Image Galleries, Poll/Surveys, Web Auctions, and search engine submitter amongst others.

HostMonster:http://www.hostmonster.com/track/hostingindex/text1

Whether you are looking to host a personal hobby site or multiple, high-traffic, large eCommerce based storefront sites, HostMonster is currently the best value available.HostMonster also guarantees 99.9% network and server uptime.

The price is only $5.95/month!!!

HostMonster:http://www.hostmonster.com/track/hostingindex/text1

Good luck!

 

I would recommend taking a look at http://www.radixhosting.com/ they will have no problem with the requirements you have. They aren't free though, but they aren't expensive either.