Programs

This is a collection of commonly-used, free tools for content creation.

Blender

Blender is probably the most used 3D tool for SL creation, with lots of tutorials and inworld help. It has a reputation for a very steep learning curve, largely because the shortcut-driven interface makes it hard to "go exploring" in the program. But if you know what you're looking for, it can provide good results surprisingly easily.
The 2.5 version sports a complete redesign of the interface, which makes it a lot easier to use, but currently, it is not usable for sculpts; for that, you need to stick to the 2.49 version.
For meshes, however... don't look back.

Primstar

Domino Design's Blender plugin for initializing and exporting sculpts. An absolute godsend. This is the tool to use if you're using Blender. Also, he has a fully rigged avatar mesh for download as a .blend file.

Jass

It seems a lot of people have problems getting Blender to run with the correct combination of plugins and Python support. Jass is a bundled package of Blender, Primstar and Python, plus some extra default sculpt shapes. If you are comfortable installing Blender plugins, or already have it running, this will not give you anything, but it has helped a lot of people getting the installation right and getting out of the gate.

Sculptypaint

Great tool for building simple sculpts. It's not a freeform 3D modeling program, but a specialized tool for certain shapes. (Including powerful lathing).

QAvimator

Easy animation tool. It is particularly good for making poses. Fluid, natural-looking animations can be difficult to achieve with the stop-motion-inspired forwards kinematics.

BVHacker

Dedicated utility for cleaning up BVH files. It more or less automatically reads and converts most quirks to something SL reads without problems, so it's a safe bet to run your animations through this and "SLify" them.

DAZ Studio

Free, quite powerful 3D modelling program, including fairly strong inverse kinematics tools. The 2.2 version writes BVH animations for SL natively, without the need for extra exporters or tools.
You'll probably need the mesh and skeleton files for the SL avatar to use Daz. You can find them here: SL Avatar.

Wings 3D

While the workflow isn't optimal for SL sculpts (though still possible), when and if meshes allow us to leverage the intuitive sculpting-style modelling of Wings, it could see a surge.

SketchUp

Similarly, while not immediately useful for SL, I am very curious what the amazingly powerful and easy interface will do for architecture in SL if and when we finally get Collada upload.

Sculptris

And just for fun, I've included Sculptris here. It's not really practically useful for realtime 3D models, but it's an amazing and fun tool with a very smooth interface, focused on just doing one thing well rather than being a general tool.