I would take him to the vet (at the very least give them a call). Take a sample of the stool if you can, too.

Well... would you be worried if you had blood in your stool?

This could be several things, some common ones are:

1. Viruses, parasites, or bacterial infection
2. Colitis which is an inflammation of the colon
3. Cancer (older dogs)

If it's a young dog, you're finding it in the diarrhea, and the dog has had the runs several times a day it's likely a parasite. Taking your dog to the vet is the best option to prescribe medicine.

If it's mild you can try fasting for 24 hours to let the walls of the intestine heal, just make sure they get water so they don't get dehydrated. I've also read that giving dogs plain yogurt also helps reintroduce good, protective bacteria to the intestines.

Best advice for if/when you do visit the vet is to collect a fresh stool sample before going. It'll save you the need for a return visit before they can do a full analysis.