I use a freeware product called “TightVNC”. There are a number of products like this out there (both freeware and cheap). Note that each of these requires initial on-site access to both the client’s PC and any routers on his side that would have to forward your connection requests.
(I know that you specifically didn’t ask for corporate solutions, but the IT folks at my wife’s place of work use a product called “Logmein”.)
IIRC, a friend who does contract IT work uses TeamViewer. The paid version has a list of your clients PCs / servers, which you can log in to whenever you need. Don’t know about $$$.
We’re mostly a custom software shop, so we need to log in to random machines for only a short period. We use the free Ultra VNC in single-click mode, connecting to a custom middle-layer that I think we wrote like, a decade ago. That way our clients just run the executable, and it reverse-connects to us. Very handy for avoiding firewall madness.
If this is with an organisation, VNC and Remote Assistance / Destop are my favourites. For a casual connection, Teamviewer allows the remote user control over your access.
I find that nothing can beat Windows Remote Desktop, performance-wise. (Although it does require some configuration on the other end. Any competent company has an IT guy capable of setting this up.)
It’s also nice enough to transmit audio over the line, where VNC (unless it’s changed a lot in the last couple years) will be completely mute-- practically that means with Remote Desktop you can hear your “new email chime” and with VNC you constantly miss new emails.
It also encrypts data by default. VNC won’t encrypt unless you go way out-of-your-way to set it up, and setting it up is a pain.