used logmein last year when I went home to philippines and had no problems. I even set up the home computer there, so when my family have problems I can easily look into it, as well as show them how to do certain things, since they are not too familiar with computer applications and such.
what OS do you have? Leopard has remote login, haven't had time to try it though :/
I find the new iChat screen sharing option being very convenient, only when someone is on the other side to accept the invite, and if all computers are on Leopard, with decent power and good internet connection.
For my own needs, I've set up a VNC server on my iMac at home, and I can access it remotely from my PC at work. In order to secure it, I use an SSH tunnel, and followed the instructions there (not so easy to set up, but it's secured and it's a one time set up, it's free and the video based instructions are easy to follow): HOWTO Use Your Mac From Anywhere
logmein is a good option, but ichat sharing works great too. you have to have sharing set up in your system preferences tho. for my wife and mom i set up their machines with my .Mac ID (they dont use .mac) so when i open a finder window i see them in the sidebar and can open screen sharing that way as well.
I haven't played with this much but, stupid question, do I have to set the remote computer that I want to access to 'never sleep'? It's a dumb question, I know, but since it generally sleeps when not in use (I like to pretend to save power) but if I can't access it unless I keep it awake - no doze I guess - then so be it.