Yep, or if its a larger wav file, you can use serial flash. Very similar to SPI eeprom (the 93Cxx series) just with great storage. Providing you're not constantly re-writing the data, reading is identical to EEPROM's. I have done with an Attiny461, an atmega88, using two high speed 8-bit PWM's mixed to produce pseudo 16-bit quality. Probably over kill for your situation though
8-bit is 'usually' good enough. You could use PWM, or an external DAC, but most micro's have PWM built in.
I converted *.wav files to *.raw format, which is a binary file with no headers (no information regarding sample rate, resolution etc..) then wrote a small VB.NET app to download this to an AVR with a serial flash memory attached. As you require multiple ''sounds' to be played, you may want to arrange your memory into sections. This means your microcontroller just has to point to the start address of a sound, and read the memory for however many bytes it is.