Edit In light of UnisoftDesign's answer: Additional clarification:
These tools make it trivial for non-technical users to set up a Remote Control connection to a support engineer. Typically, both sides are behind a firewall they have no control over. Noone involved has to deal with IP addresses, ports or any technical stuff. Both sides just open an app, and one side has to enter a number. That's it.
One crucial point with these tools is also that the support engineer and the user see the same desktop.
What I am looking for atm. though would be a product that gives a user experience on par with above tools, but one that is self-hosted, that is all data transfer only passes through our servers.
I had a few hits through Google, but having someone recommend a tool who's actually used (and administered) it, would be far more useful than the marketing fluff on the company sites.
Note: The reason I'm looking for a fully self-hosted and self-controlled solution is paranoid IT departments, so there's really no arguing.
Edit: Hmmm ... given Combo's answer and my own Google Searches, it seems I could also have phrased the question: What other decent tools beside ScreenConnect are there?