AMD Mobile Sempron 2800+, 1.6 GHz (SMN2800BIX3BA)

The CPU I received is actually a 3000+, it also runs at 1.6GHz but has a little more (256k) on-die L2-cache memory.
It was installed with the stock cooler in a basic motherboard which has only simple overclocking features but is stable at 2400 FSB which gives a CPU speed of 1.9GHz. The board will not go any faster and there is no facility for voltage adjustment so there's no way to go faster, but still this is a useful increase.
To give an idea of performance, Bioshock at 1200x960 resolution ran at 30fps average with all visual effects on full. (X1950 and 2x1GB DDR2-5300)

Some online forums and reviews suggest that this CPU will go way faster, even up to 3GHz with good air-cooling.
For someone with a decent AM2 mobo and good cooler, like the Arctic Freezer 64 Pro, a Sempron could be a good budget buy as it should be easy to crank it up to match the performance of an Athlon 64.
Those not bent on overclocking and looking for an efficient CPU should opt for
the models that support the "cool'n'quiet" feature.