I have been working on a project which uses 12 volt dc solenoid valves. They were causing problems with the arduino due to feedback so I was advised to install flyback diodes across the coils and that solved my problems. I'm upgrading the solenoid valves in my project from 3 way to 4 way valves and the new ones have a DIN connector which already has what appears to be a capacitor across the coil terminals (as well as a resistor/led indicator). Does the capacitor negate the need for a flyback diode? If not should the diode replace the capacitor? Any info would be appreciated.
I would not be surprised if those were MOV devices in there instead of a capacitor. A coil/capacitor combination is known as a resonant circuit 
What you are probably seeing is one of These MOV parts The diode (or MOV device) will dump the energy from the flyback when the power is removed from the coil. If that were a capacitor, you would see a ring (like a bell) if you viewed it on an oscilloscope.
So it's doing the same job as the diode that I had to add to my other solenoid and I should be able to use it as is?
A MOV does not do the same job as a diode, but its effect is similar.
If the part is a MOV, whether the designer's choice is correct for your Arduino circuitry is a different question.
The only way to be sure is to use an oscilloscope and check for large transients across when the solenoid is turned off.
If you continue to have problems, replace the part with a flyback diode.
The advantage to using a MOV part (which may explain why that could be it) is that it does not care if you reverse the polarity of the drive to the coil (or even use AC - it clamps at the specified voltage - kind of - sort of a soft clamp). If you have the polarity of the drive reversed to the coil with a flyback diode, the diode will conduct all the power instead of the coil (hopefully a fuse or other protection will prevent letting the magic smoke out :o ) Remember the weakest part of a series circuit is known as a "fuse" !!
Remember the weakest part of a series circuit is known as a "fuse" !!
Or anything but the fuse!! 
LarryD:
Or anything but the fuse!!
Yes, driver transistors are known for blowing to protect the fuse :o
gpsmikey this particular DIN connector is also used for solenoids with AC coils so based on your explanation I guess you are correct in assuming it's a MOV. So, just so I'm clear.....it should help with the issue of spikes from the coil collapsing affecting the microprocessor but if I still have that problem I should replace the MOV with the same diodes that fixed the problem on my old solenoids, yes?
Correct. MOVs dampen the spike. Diodes essentially eliminate it.
... and MOV's won't slow the solenoid's response on release, a diode definitely will.
I'm thinking that the built-in MOV will clamp enough of the interference that it would not cause a problem, so either method should work.
MOVs wear out, a TVS is the correct choice for frequent (unbounded) number of transient
events and TVS's are available at more appropriate voltages (lower, less interference)
Just add your free-wheel diode as before is probably the simplest course of action with
least risk.