A good place to start is the idea that strong photos come more from light, composition, timing, and post-processing than from the camera alone.

From the examples mentioned:

• Wilson Tsoi is cited as making excellent images with a Canon A620, a low-cost compact with manual controls.
• DigitalRev’s “Pro Photographer, Cheap Camera Challenge” videos show professional photographers producing impressive results with very cheap or limited cameras.
• Lee Morris also demonstrated a fashion shoot with an iPhone 3GS, showing that even a very basic small-sensor camera can produce strong images when used well.

One practical takeaway from the answers is that cameras with at least some manual control are especially useful for learning creativity and technique on a budget.

So, for inspiration, look at challenge videos featuring skilled photographers using cheap cameras, and seek out compact-camera shooters whose work emphasizes composition and light rather than technical perfection. Those examples can help beginners see that the photographer matters more than the price of the camera.