I'm lost on search terms here so thought I'd toss it out:
Say you have a drupal site at site.com that accepts user registrations. When bob signs up to site.com, he gets a nicely cloned drupal install pre-setup with a bunch of views and content types and whatnot via some install profile and an admin-but-not-user-1 account, accessible at bob.site.com. Multisite perhaps? Total not-sharing of tables/content.
Having never even come close to this before, what should I be looking for and is there something out there that does this already? I'm guessing sites like drupalgardens do this.
I probably shouldn't try and research silly ideas like this when I'm sick and my brain isn't quite functioning >.<

Comments
I use BOA
I use BOA (groups.drupal.org/boa) to manage the server and accounts. You can send commands to BOA to set up sites, backups, etc..
It also has an auto aliasing option to create bob.site1.com
And you can add domain names, etc.. later if required.
For the standard setup - use a profile. Setup a site the way you want and save it with features/strongarm. Then essentially place that file in the profile folder - there is a little more to it.
I decided to keep most of my customisations in Features rather than forcing at install.
My 2c and some more
First off I would suggest that you have site.com selling the sites and sites.net for the customer sites, otherwise someone can (and will) setup support.site.com or sales.site.com etc. I would even go so far as running site.com only with an EV SSL cert.
In order to make this all work you will need something like aegir or a collection of scripts triggered by rules that will deploy the site. Your installation profile should use some services calls on site.com to get the data to populate the initial site build.
In terms of having a non user 1 admin role, I'd suggest the following:
If you're serious about creating such a service, expect to invest heavily upfront. The only service which has been at all successful has been Acquia Gardens and now they seem to be focused on enterprise clients. Others such as buzzr and subhub lite have failed to really take off. Wedful is still around, but they are targeting a very narrow niche.
I wrote a blog post series on being about spit out Drupal sites for $100 each you can find it at http://davehall.com.au/blog/dave/2010/12/24/100-drupal-site-series-part-... I seriously considered building such a service a few years back. These days I think you're looking at more like a $250 sticker price and needing several 100K in up front investment.
There isn't much info in your post about the idea and business plan, so I can't really provide you with any more specific advice. I'll be interested to see how you go with such a venture - please blog about it as you go.
I wasn't thinking of this for
I wasn't thinking of this for site hosting (you're up for a tonne of tech support with that) but for a SAAS written in Drupal. Where I work could use some kind of automated hosting with the same mechanism but that's not my call to go ahead on.
Just the system to set this up without getting into the specifics of the profile you set up is a project on its own, and if anyone else is interested in giving me a hand I'm very much open to helping hands!
Some excellent advice there though Dave (and geoff!), thanks :)
Oooh
Hah, you just made me look up the domain I was thinking of putting this on. The .net is free! buys
Its one of those great domains that makes me think I've spelled it wrong because it was free when I bought it ...
Similar project
I've been talking with a client about implementing a similar system. They want it for internal use, so each of their branches can create sites, but I think it will be very similar.
I would be happy to be involved if you're interested in getting a group together.
For prod?
Would each branch create a production site? Or would be more like Lullabot's git pull workflow and creating QA sites per branch? If it is the latter you might want to look at WFTools. WFTools creates a sandbox per branch and handles the merging through environments.
Self promotion eh :P
Each magic new site would be ready to go instantly, the idea being they just use the site as-is rather than using it as a base to develop from. This is why I want the main user to have less-than-admin permissions. Honestly, they don't even need to know it is Drupal.
I have a minion onto this (this is why minions were invented, to carry out evil schemes such as this) and I'll point them at WFTools and the others in this thread and get them to play around, I think it'll take a while to figure out what tool works best.
Incidentally I could use
Incidentally I could use consulting on this too, but this isn't for work and I'm cheap so I'm thinking instruction on telling my minion what to do rather than paying for work done. I honestly don't have the time to get into it myself.
Feel free to get in touch if you've implemented something similar before.