My company hesitated to buy TeamViewer licenses because they're relatively expensive. We stretched the free use, and accumulated a bunch of throwaway Google accounts for Google Remote Desktop, and futzed around with LogMeIn and Hamachi appliances.
Then we bought a batch of TeamViewer licenses for our Controls team, and they've saved us tens of thousands of dollars in travel and lodging, and saved our customers downtime measured in the millions.
I use Google Remote Desktop to get between my home PC and my work PC, but I use TeamViewer for every connection to a customer site.
I realize your post specifically said "no TeamViewer, and no firewall configuration", but I can't recommend that. TeamViewer has been the easiest to set up, most reliable to maintain, and has the best feature set (VPN is essential and file transfer is pretty good).