Well first off we use 4 methods for remote connections - VNC, GotomyPC, VPN and Remote Assistance (built into XP).
Our department (IT) is on the first floor, our main operations happen on the second floor so on our LAN we use VNC a lot to remotely administer stations on the second floor, helps save us the trouble of running up and down stairs all day long.
Now you are mentioning a scenario of supporting clients outside of your company (and your corporate LAN).
We have Sales people that work remotely from home and we have an afterhours staff (because for an added fee we promise our customers a 24/7 support staff) and they also have offices from their home or work on the go with laptops.
Gotomypc is good and relatively cheap solution for lightweight remote connections that aren't of a critical security issue. Let me make this clear -- because the gotomypc folks will sell you the service under the terms that it is secure...IT IS NOT SECURE! The only security that happens on a GotomyPC is at the application (Web Browser) level, it secures the "handshake" (for lack of better wording) with SSL 128 bit....HOWEVER the connection itself that is the actually communication path the data is traveling is no more secure than a basic LAN connection.
So if you want remote connections and security is a concern for you...go with VPN. The other options are much easier to get up and running, but VPN rules them all in terms of security. Remember the entire "path" is secured with VPN (hence the term "tunneling", you are communicating through a PRIVATE tunnel).
Assuming your company knows enough to have purchased a hardware firewall solution that is at least half decent, even if only a few hundred to just around $1,000...its VERY popular these days for firewalls to include VPN ability, in fact its harder to find a business grade firewall that DOES NOT offer VPN than it is the other way around.
So you may own the "solution" already and not even know it -- check out your firewall hardware, look at its documentation.
Hope this helps.
Tom