Nathan Seidle, founder of SparkFun, recently told the story of how his business started from his bedroom in 2004. Since then, there has popped up a lot of good suppliers of electronics and other maker parts online. Here's a short list of some of them. Feel free to send me more links. Since almost all of these are US based, sites from Europe is especially welcome.
Very well equipped online electronics shop, with smooth ordering process. They stock basic components, soldering kits, robotics, Arduinos, and also produce several breakout boards and other items themselves. In Nate's own words, "SparkFun makes technology more accessible."
Furthermore, they have established healthy community, with comments and discussions on both the product pages and forums
Grown out of the MAKE Magazine, Maker Shed have lots of different "projects in a box", or kits; a little bit of everything. Including electronics, crafts, and chemistry sets.
More components, kits, boards, and Arudinos. Focusing on robotic kists and solar cells.
Electronic Goldmine "specialize in purchasing inventory lots directly from manufacturers and companies that build electronic equipment". A very good selection of basic components at good prices, however with changing inventory from week to week.
Get your moving parts from ServoCity; including steppers, servos, DCs, and accessories. As well as other mechanical parts shaft couplers for your motors. Furthermore, they stock an extensive selection of batteries.
McMaster Carr has a wast selection of mechanical and electrical parts, as well as utility hardware.
Finally, the only non-US shop on the list for now; Conrad Electronics from Austria. They have web sites and shops in several European countries. They have a broad assortment of technical parts and kits, including consumer electronics, computer, hobby, lighting, and RC kits. Their selection of batteries is impressive.