I've used sharelatex in the past, and it is really useful.

I'm one of the co-founders of ShareLaTeX, and there are two main reasons that we've found that people really like ShareLaTeX. The first has been mentioned - you don't need to set up a LaTeX repository yourself. Even more than that, you can work on LaTeX documents from anywhere. It tends to be hard to find LaTeX installed on a computer if you're on the move and not using your own machine.

The other advantage is the ease of collaboration. While there are plenty of people in the LaTeX world who know git, there are plenty that don't as well. ShareLaTeX gives everyone a point and click way to make sure they are in sync with their collaborators. That said, we're getting quite close to offering git access to the projects for people who want it.

Also, my apologies that we keep appearing on the front page (along with a few other similar sites). We're flattered that people keep submitting us though.

You don't need to learn git/svn and you do not need to setup a repository.

Yes, we have a feature called 'History' which you can access from the editor. It lets you see the changes that have been made to your project over time. It's a bit of minimum-viable-feature at the moment, but it's still quite useful, and we're always open to feedback on how to improve it for your needs.