The SPN1001-FV1 from SPIN Semiconductor is an ever-popular choice for effects pedals. The FV1 chip is powerful, easy to program and has analogue inputs and outputs, making it simple to design with. Also available is a low-cost development board with lots of code examples and algorithms to download from the SPIN website.
Experimental Noize's FXCORE chip is a powerful Audio DSP dedicated to creating audio effects for professional audio applications.
The NJM8202 is a low voltage rail-to-rail audio op-amp. Excellent RFI immunity ensures your audio signals are not affected by mobile phones and other sources of interference.
The THAT4316 Analog Engine will make a great sounding compressor running off a battery.