This post will continue to be maintained to contain the best free utilities and downloads available for WSS and SharePoint 2007. Add your comments and submit your nominations!
To "look under the covers" and diagnose tough issues you need a tool navigate directly into SharePoint's object model. The best not only show you what solutions, features, and event receivers are activated everywhere, but also let you dig into the actual configuration settings on each farm, web application, site collection, site, list, and list item.
SharePoint Manager - The first tool to break from the rest of the CodePlex pack by "just working." SPM provides additional power (and danger) by also letting you change each property.
SharePoint Analyzer - The first free scoping tool released by a company (Bamboo Solutions). That doesn't imply it's going to have a better lifecycle than a community project, but Bamboo has a pretty good track record of providing good product and this started off in good shape. And the latest (1.1) supports x64,
Improvements and extensions to the out-of-box features
Starter Kits - Think of the Community Kit not as a tool to create community sites, but as community-supported improvements to SharePoint. So yes, there are great, complete templates for user groups, schools, weddings, and home owners associations, built by people who actually needed, built and used them (unlike the "we'll get you 65% of the way there" Fab 40 demo-ware). But the real gems for the masses are the new discussion, blog and wiki features to replace the anemic out-of-box versions. Head to the Releases page and look in the box at the top-right to get what you're looking for.
Faceted Search - The people responsible for Search did something unprecedented by releasing not just fixes in service packs and the infrastructure upgrade, but significant new functionality. Faceted search is a contribution that didn't make it into the "officially supported" product set, so they pushed it to CodePlex and continue to update and improve it (v 3.1 as of Jan '09). You can read more about it in the team blog (Part I), though the CodePlex page has pictures to see why Faceted Search is so useful.
Scot Hillier's SharePoint Features - Where the starter kits (above) enhance SharePoint's built-in features, these add what was completely missing. The Log Viewer must be the most popular; anyone who's ever slogged through the ULS logs can instantly appreciate it's ability to filter out the bazillion "Preserving template record with size [x], use count [y], key [z]" messages. There are dozens like that - a toolbar manager, task mover, appSettings manager, theme changer, hierarchical views of content types, and more all the time.
Gary LaPointe's STSADM extensions - These extend the command-line STSADM tool with loads of new commands. First, check out the big list of all the STSADM extensions in here, there are over a hundred. Enjoy.
Visual Studio project templates (STSDEV) - This tool generates projects for all the common SharePoint project types. They're all based on plain old class files, so unlike VSeWSS, STSDEV doesn't require special project types installed to VS to use the projects you create with it. they're also compatible with the next great tool. . .
WSP Builder - So you've bought into SharePoint's great deployment model - everything should be packaged as a SharePoint Feature and SPFeatures should be wrapped up in WSP Solutions. But you'll have to do that by painfully editing a DDF manifest by hand, ugh. WSPBuilder to the rescue! Just point it at a subtree including your deployment files (sorted into .\GAC, .\80\bin, .\12\... anda few others) and bam, instant WSP. I like to add the "/Cleanup false" parameter to leave a copy of the generated manifest where I can see it too.
U2U CAML Query Builder - SQL Server would be hell without it's query builder (and to think the idea had to start with MS-Access), so why write CAML by hand? Thanks to U2U we don't have to. There are a bunch, but this one has a track record of providing good features, a reasonable pace of updates and stability.
Reflector - Lets you see every class, method and property in a .NET assembly (DLL), with the option to translate the MSIL into readable C# or VB code. Not that anyone remembers ILDASM, but this is everything it didn't do and then some. Written by Lutz Roeder and later acquired by Red Gate to (presumably) assure its continued development. Trying to figure out what version is installed to production, but every assembly is still marked 188.8.131.52? Reflector lets you look inside to see the code that's there. Trying to figure out why you've been leaking memory ever since you installed that third party web part? Oh look, they're not disposing of their SPSites. I can't imagine working with .NET without Reflector.