When to replace a tire?
Yes, it is time to change that tire!

Your current front tire looks to be in very good shape so when you purchase a new tire you should put it on the front wheel and then move the old front tire onto the rear wheel.

Continental road tires have helpful wear indicator dots on them that will show you when the tread of the tire has reached its recommended replacement point:



There will be two of these indicators on the tire, one on each side of the tire's center line. Note, they are not always quite this close together. Many other brands will also have such some type of indicator marks on them, especially road tires and other tires with no to light thread patterns.

For other tires there are some general rules you can follow on when to replace a tire:


You start experiencing a sudden increase in the number of flats received in a tire and there are not good explanations for the flats. 
The tire has worn down to the point the casing has started showing through the tire. 
On bikes where your tires have noticeable tread pattern (mountain bike, cyclocross tires etc.) and the tread pattern has worn down. 
You have a long, wide flat spot along the centerline of the tire, such as in your photo. At this point you may also notice your speed has dropped of slightly and that cornering may have gotten a little squirrelly. 
The tire has cracked rubber, either due to the age of the tire or mistreatment such as improper storage or consistently riding on the tire while it was under inflated.


Some people will try to give out general milage estimates of how long a tire should last but these tend to be pretty useless as your tire's longevity depends on the type of tire, your riding style, your riding conditions etc. 

It is typical for rear tires to wear more quickly then the front tire. I have always attributed this mainly to the fact all your starting force is applied to the rear wheel hence any wear due to friction while starting and accelerating is experience on the rear tire. 

This answer to the question 'why does my back tyre wear so much more quickly than the front?' also postulates increased deformation of the turning rear tire  results in more wear due to the sliding of the tire that occurs during the deformation process.