Low-hanging fruit is the easiest to gather; always look for the easy solutions before you move on
I have been a SharePoint 2007 admin/developer for about a year now, and I have learned a LOT. I have also spent countless hours tracking down strange and seemingly causeless errors in SharePoint only to find out that 50% of my problems required a simple 5 minute (or less) fix.
Here is my list, hopefully this will save you time.
ALWAYS try these before you go on to crazy or overly involved solutions.
1. Run an IIS Reset
This is the simplest and often reflects changes that were made that might not show up right away. Simply open the command prompt on your SharePoint machine and type iisreset. This will cause momentary downtime (a few seconds) if you are running a single WFE.
2. Run 'SharePoint Technologies and Configuration Wizard'
Only #2 on the list because it takes slightly more time than #1. On the other hand, this has fixed more problems for me than any other on the list. This does automatic IIS resets, so you will have temporary downtime on a single WFE environment.
3. Reboot your machine(s)
This seems obvious, but for some reason is often overlooked. This holds as true for SharePoint as any other Windows OS/application; the only problem is potential downtime for your users, but if you have more than one WFE, it shouldn't be a problem.
4. Make sure account has proper rights
This one is more for stsadm operations and scripts, but most of the time I have found if a command is giving you some strange failurethat it shouldn't, it is more often the account you are using doesn't have the specific right you need for that operation. The command line runat command is your friend for testing this.
5. Install most recent Service Pack/Update
Be sure to check with Microsoft for any updates. SharePoint is one of their most premier products at the moment, and they are spending a lot of time and money developing for it.