In DoD side, they tend to use DameWare. It was stagnant for a while but has gotten better and even has a linux client now. Think "ugly but powerful".

I've seen fly by night engineers hurdled by IT deps using TeamViewer way more than I would ever want to admit. It "just works" but doesnt have many of the management features.

I had an awesome experience with on-prem ScreenConnect, but then they changed their licensing and names and all kinds of other things. Nice featureset, writing plugins was easy. I still might consider it if I could get a decent deal.

Bomgar was pretty polished and has some interesting mobile/mdm stuff in the works last I tried it, but that was a long time ago.

GoToMyPC and LogMeIn both tend to be favorites of MSPs for some reason, I never really liked them mostly because of the management interfaces and constant license changes.

Citrix really seems more focused on real enterprise. Features are nice but the price reflects it, good support.

RDS/Terminal Services in the windows world is a staple, just have to watch for licensing violations which happen a lot. Lacks a lot of the management features other things have, but is built in.

Then you get into open source, which really comes down to some variant of VNC (choose your poison) which is really all just remote desktop with no management features. There is also noVNC and Spice which are pretty cool and used in more and more foss software (like proxmox for example).

There is Apache Guacamole which is like a gateway to access RDS/VNC et al instances, which is pretty cool.

So yeah, it really all depends on your use case and budget.