If you’re trying to connect from one (Leopard) Mac to another, you can use the built-in Screen Sharing functionality; turn the server on from the Sharing System Preferences pane, and either use the network browser (on a LAN) or just open a vnc:// URL.
If you’re trying to manage a bunch of Macs, try Apple’s Remote Desktop (ARD) software; it’s sold in 10- and unlimited-client versions, so if you’ve got fewer than 5 or so Macs it’s probably not worth the money. The client bits for ARD are part of OS X. Screen Sharing and ARD use the same protocol, which includes some Apple-proprietary extensions to VNC which do encryption (either of all data, or of just keystroke/password info) and support adaptive JPEG compression, which gives you decent-enough performance (usable, but nothing like RDP or NX unfortunately).
If you need something cross-platform, check out Timbuktu and TeamViewer (which will punch through firewalls and so forth).
In some situations Copilot is a good solution. Not so much for day-to-day admin, but great for remote tech support.
If you need the solution to be cross-platform (ie, controlling an OS X box from Windows) then VNC is the obvious choice. I’ve had much better luck with the free Vine VNC Server than with Apple’s built in one. As for viewers, Chicken of the VNC on OS X or Tight VNC on Windows are good solutions.
As others have said, for security firewall VNC and then use an SSH tunnel. There’s lots of ways to do that, and the exact details depends on OS, firewall, network, etc. One method of creating an SSH tunnel for VNC is described here.
Apple’s Remote Desktop has AES encryption. Another good way is to just enable SSH in sharing and use shell access to perform tasks without interrupting the user.