Microsoft has done a nice job of providing several upgrade options for SharePoint installations. For those running 2001, there isnt an upgrade path, expect thrid parties to provide a solution.
The Microsoft’s team design goals (Posted by were as follows:
  • Provide clean v2/O11 to v3/O12 upgrade: No upgrade plans for v1 – v3/O12 release
  • Minimize user impact: Reduce outage duration, Limit number of users impacted for any outage
  • Support customizations to v2/O11: Custom site definitions & web parts, Pages customized using FrontPage
  • Provide resource use choices to admins: Enable upgrading existing farm, Support migrating to new farm
  • Provide single clear set of UI options: Both GUI and command line, Consistent approach for both products
Before upgrading, always do the following as a minimum:
  • Create a plan, do your research
  • Verify your backup and restore process actually works
  • Communicate with the user community
  • Decide how you will deal with custom webparts and site temaplates
  • Perform two full backups
The options are as follows:
  • Gradual – This will allow the existing installation to function and enable you to upgrade web sites in batches. This option allows coexistence of new and old but is more resource intensive. Best for large 30GB of content and beyond, test your upgrade process for customzied sites and web parts. Most large organizations go this route due to service level responsibilities and mitigating risks associated with upgrade (Customizations are your enemy). 
  • In-Place Upgrade – All Websites and databases are upgraded at once. This option is best for installations with 30GB or less of content.
  • Do not upgrade – Can be run along side existing installations.
  • Content database upgrade – for large installations where you want to consolidate farms. Consolidate your content databases in one location and Point MOSS to the databases and an upgrade will begin. Expect large corporations with TBs of data to take this approach
Micks’ Breeze blog provides screen shots of the upgrade process. The SharePoint Almanac also has screen shots and more information about the upgrade process.