Please use this thread to consolidate your useful links that have helped troubleshoot OSX problems.

The most basic steps are to restart in Safe Boot and Repair Permissions.

Mac OS X 10.2, 10.3: How to start in Safe Mode

Repairing Permissions

File System Check and Repair (fsck) more details what "Safe Boot" is doing

OS X 10.2 Jaguar Troubleshooting Written for the average intelligent user: taught me more about using OSX than anything else I read

Apple now has a very useful page for Isolating OSX issues

Connection Problems:
Check here to find out connection Test speed for uploads and downloads

Mac OS X: Troubleshooting a cable modem, DSL, or LAN Internet connection

Upgrading Router Firmware Also has a good link to check for router upgrades

NAT'ed? A very handy guide by Kurt Meinz for those sharing one IP with a number of computers, written with Gnucleus in mind.

Ports open? I test by downloading Chris' checknat.app.sit, (originally written for Acquisition) but it works when LW is running too.

[edit] Thanks to Ursula for the highlighting suggestions