Connectix/Logitech Quickcam - The Classic

This camera comes in a variety of models: Grayscale, Color, Color 2, Pro and VC. Some are USB, some are Parallel. Unfortunately, most models are discontinued.

Dave Allmon's QCV2 allows you to make timed exposures on older grayscale quickcams.
Linux Third Party Quickcam Driver page.
AstroCam's detailed Quickcam information.

Philips Vesta - The New Guy

This color camera comes in a variety of models, all USB and is priced around $45.

AstroCam's detailed Vesta information.
Linux driver for Vesta Pro. Also allows up to 1 second exposures (Linux only).
The impossible made possible: Timed-exposures with modified Vesta!
How to do the impossible, Step by Step. Need Vesta long-exposure software for Linux? Check out Cat's Eye.

Software

COAA's AstroVideo video integration software. Exceptional product. Limited trial.
Dave Allmon's QCV2 allows you to make timed exposures on older grayscale quickcams.
Colin Bowne's Vega 32-bit capture software. Indispensable software for all cameras.
Iris image processing software. Extremely powerful, yet complex image processing tools for advanced users.
AstroStack image enhancement software. Allows you to stack and enhance a series of images; BMP or AVI.
Not necessarily astronomical, AVI2BMP is very useful for processing your night's work into a usable format for software processing.

Accessories/Hardware

Stephen Mogg's Universal Webcam Adapter. If there was a prize for the product of the year, this would be it. If you're using a Quickcam or a Vesta Pro, you need this product.
One way to Peltier-cool a Quickcam.
How to make a Battery pack for a quickcam.