Do chips exist that act like little programmable pulse generators?

Like use I2C/serial to say, "on pin 4, have a frequency of 400hz at a 30% duty cycle", and have the chip do that.

 

Microcontrollers.

It's easier to program a dedicated micro (or even integrate this into your application) than to find a custom chip.

You can easily purpose the timers to do this, or even the PWM module on some chips.

 

Not sure if this is useful, this PIC program could be modified to do what you want.
http://forum.allaboutcircuits.com/showthread.php?t=40875

 

Many dial tone controllers have been developed for simple tone generation. ML2035, PCD3311, M991 come to mind. May be of use to some if they still exist.