Arduino 300 Outputs

You'll have to put your own diodes across the relay coils, to dissipate the coil generated current when you de-energize the coil. The TPIC6B595 datasheet says
"The device contains a built-in
voltage clamp on the outputs for inductive
transient protection. Power driver applications
include relays, solenoids, and other mediumcurrent
or high-voltage loads."
and it shows test results for a 200mH load, but how much are relays really?
I use this one on a board I offer, but I don't see a mH rating, so I use a diode across the coils, and have not had a problem.