MySQL database across multiple servers
Solution 1:
You can indeed, 'tis MySQL Clustering you need.
One feature in particular - "auto-sharding" - will spread your data across multiple machines. "Online scaling" allows you to add new nodes if you need more capacity while the db is running. Pretty cool. You can download it here.
However, there are a few other things you can consider to resolve the problem, which may be easier to achieve:
Get a bigger hard drive!
Sounds a bit obvious but if you could safely say that a xxxGb hard drive would last you Y years then it might be worth going for. You could either take an image of the drive and install it on the new one, or you could install it as an additional drive and move the MySQL data files to the new drive.<
Split the tables across multiple databases.
Split tables across multiple databases, which can then be stored across multiple drives. Windows Azure has size limitations on its databases and Microsoft recommend this approach. It also improves performance a little.
Can you archive data?
Are you able to archive large tables onto another drive? Is the data really needed? If it's historic and only required for reference can you set up an archival process that pushes it into files on another drive, or into archive tables in another database that points to datafiles on another drive?