Arin,
Yes on most systems supplied now you will see no limitations on Bandwidth, file limitations and database numbers, many of the more popular hosting providers provide these now. BlueHost, Hostgator, iPage, etc.
Now one thing to keep in mind when they say no limitations, they mean reasonable limitations. No hosting provider is going to let you upload Tera-Bytes of information to their servers, not without a very hefty fee. That is just being realistic, if I have 50GB of dedicated storage, that is more that enough for a extremely large site. Now if you are hosting a PHOTO Studio site, Movie Studio Site, where you have very large files, you may expect to pay a little more for storage, just be realistic in your expectations.
Same thing with Databases, if I can set up 50 to 100 databases that is plenty for any large site. The key with databases is to make certain they are setup correctly and normalized.
On the control, on a shared environment you will not be able to control what is one the server, nor would you want too. I do not want anyone uploading applications that are running on my hosting server that have not gone through a ton of security and comparability checks with that server and ever piece of software that is installed on it.
What I do want to be able to do, is with the support software installed on that server, Apache, PHP, PERL I want to be able to set their configurations for my portion of the server. There may be certain error checking that I want enabled as I develop an application, there may be certain Cron Jobs I want to run at different times, all this is possible with a good provider. Again, most of the providers now, with the way that they setup the Virtual environments have no problem with offering this.
Of course, as a side not. Be careful what you wish for....
Having these abilities also come with some responsibility. I have brought down one of my own sites a couple of times changing configurations on the Server and the Database environment, trying to make things better, speed things up, and not completely understanding the unintended consequences os some particular settings. SO whatever you do, before you make changes to your environment.
1. Understand the change you are going to make.
2. Read, read, read on the impacts of the change.
3. Back Up your system, off the web server. (DO NOT store your backups on the web server, you may not be able to access it)
4. Make changes incrementally, one change at a time. Test the change, confirm the results, then proceed with the next change.
I hope this helps.