Heyyo, guettli. I too looked into this recently.
Apache Guacamole claims to be "a clientless remote desktop gateway." Clientless, they say, means no client software or plugins. Guacamole is open source software.
Ajax VNC also claims to be "clientless" & "purely HTTP."
Appear.in requires no software, & is browser-based. Appear.in is my 1st recommendation as it meets your standards! Also, it does not require login or installations on either side. You just need to set up a room. Voice & text chat, private rooms, & connect using link are nice features. Supported browsers are Google Chrome, Firefox, Vivaldi, & Opera.
xrdp is an open source remote desktop protocol(rdp) server. It is "capable of accepting connections from rdesktop, FreeRDP, and Microsoft's own terminal server / remote desktop clients."(xrdp.org/). It is based upon FreeRDP & rdesktop, and uses Xvnc or X11rdp for management of the X session. X11rdp-o-Matic will automatically setup X11rdp & xrdp for you. Xrdp is my 2nd recommendation.
If you decide that downloading would actually be okay, then I suggest TeamViewer 11. I personally use TeamViewer to help my cousin resolve computer issues. After getting to know how to use it, I love it! It supports Linux-Windows-Mac OS X. Chrome Remote Desktop would be my other suggestion if you do decide downloads are okay.