I personally use LogMeIn Rescue for all of my remote support needs. I support about 250 machines, in 3 office locations (Los Angeles, New Jersey and Canada) as well as sales reps in all 50 states, as well as the Caribbean.
While on a LAN, I can directly connect to machines without the need for credentials (assuming that is how you have it setup) and for those machines off the LAN, you can install a "calling card" on their desktop, that the user will just click on, and it will start the session.
Built into the UI are pretty much any tool you would need. From file transfers (both ways) to a task manager, report viewer and of course desktop control.
You can set up multiple users to have more or less control depending on how your organization is set up as well.
No, I am not in any way affiliated with logmein, I just use their product and it works very well.
Previously we used Cisco Webex, and to be honest this works a whole lot better for a whole lot cheaper.