It depends on who your provider is.
Most shared hosting providers offer "unlimited databases", what they restrict the most is CPU.
If I had to choose shared hosting, I would probably go with Dreamhost, for $10/year, they offer a great service(coupon needed, $97/year otherwise)
There is an advertised "limit" at the host I use, but I've routinely gone over it (one or two by a huge margin) and never have gotten billed for overusage. I don't think they monitor it like they do the actual web server, as we used our databases out of a shared pool of separate database servers.
We had to a VPS at the same host for a couple of reasons, so we don't have any limits unless we fill up our quota of hard disk space.
I thinkWebHostingTalk.com is a good way to find out about host. More then often you'll get a good idea doing a search there, if the host you have or you are looking into; is something worth the value & effort.
Typically you want to avoid anything that says, unlimited. At least until you can find me an unlimited hard drive. (or unlimited CPU and Ram resource)
However for shared hosting, I found that HawkHost.comis highly recommended and I've used them. You'll find some good reviews online if you do some searching.
That's true. Our host specifically gives us a limited number of databases. They do state the size of them also, but it is not yet enforced (and they've had these shared database servers since the late 90s IIRC).
When you get into VPS or dedicated, I've found that databases are pretty much unlimited.
I have actually been looking at the cloud services like those Amazon offers. I know they offer databases in the cloud (I think it's Amazon RDS), and I believe you could actually host a full site online as well. It probably has some shortcomings but the nice part is fault tolerance: if one server goes offline, the others pick it up and your site is still seamlessly online. It's also a "pay for what you use" model, so you have to be really careful to estimate your usage before you hand over the credit card.
I have a reseller account with HostGator. I have been with them for many years. I have never had a resource problem with HG. I have always found their support and resources more than adequate for my needs. The owner, Gator Brent is very pro-active in customer service. If you can't get a resolution, I have observed that he will honestly try to help. I had a sticky problem with my ISP a number of years ago. They blamed the problem on HG. I called HG's support line on a Sunday morning. Brent returned my call personally. He had the problem solved in very short order. It did turn out to be the ISP's fault and not HG, but he followed through anyway. I have also heard that he treats his employees well but can't say first hand.
I have my VPS servers at Linode.com. They are awesome! I tried HG's VPS's while they were in beta. I prefer the xen based offerings with Linode or others instead.
A nice feature with both HG and Linode is the ease of expansion. With HG, they will upgrade your account and handle the transfer proficiently. With Linode, it is just button press away. Everything is automated. You can increase all of your server resources to ridiculous easily and quickly.