Chain slips to lower gear when pedaling backwards I have a hybrid 18 speed bicycle which is able to shift through all gears on both the front and rear sets of gears.  When on the largest gear on the front set (by the pedals) the chain will try to slide to the next smaller gear when pedaling backwards.  It is as if the chain in bent or not moving in a spot.  

There is also a cyclical click when pedaling forwards in higher gears with an occasional slip.  It seems the chain may be uneven in several links.

What is the most likely cause/fix for this?
This sounds like a stiff or separated link in your chain.  There are other options, but this would be easy to eliminate, and a likely cause. 

Get off the bike, and very slowly pedal backwards while looking at the chain as it passes through the rear derailleur. 

A stiff or broken link should jump as it goes through the derailleur. 

If the chain starts to come off the gears, check the chain at the point where is is coming off. 

Most likely, you will need to replace the chain. If the chain is new, the link where it was joined may be the issue. In that case gently flex the chain side to side (against the link plates, not in the direction they pivot) at that point and it may free the stiff link. 

If not, replace the chain, taking care to join the links more carefully this time.