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I've used Chrome remote desktop for a while: https://chrome.google.com/webstore/detail/chrome-remote-desk...

iMessage (via Messages.app) has remote control/screensharing built-in :)

And, unfortunately, like other Apple services (like Back to my Mac), it suffers from access to computers behind routers.

Computers behind routers? So... all internet connected computers then?

I use Back to my Mac from work all the time and I have no problem accessing my iMac at home from my MacBook Pro at work.

Actually, yes. I used to be an Apple Genius and whenever we dealt with two machines on separate LANs, that required NAT, there were so many problems with traversing the routers. We had to do manual setups with port forwarding or DMZ. Facetime seems have significantly improved with this (but was awful when it was iChat w/ Group Video chats), but Back to My Mac is still very problematic-- you can see this issue also by trying to Screen Share over iMessage to other people. In my experience it only has about a 50% success rate.

My home setup still doesn't work with Back to My Mac (and hasn't for years).

LogMeIn or ScreenConnect if you want to pay for a solution.

Nothing else I know of is free.