Take a look at necrotizing fasciitis. The infection progresses quickly (think hours) and decays the flesh like gangrene. It's spread through contact with open wounds and the treatment is antibiotics and/or amputation. Necrotizing fasciitis doesn't typically affect healthy people, however, a mutated form with increased antibiotic resistance would be dangerous to healthy people especially if introduced directly into the bloodstream through a bite for example.
Mucormycosis (a fungus) is also pretty cool for the purpose of zombie scenarios, because it affects the brain and skull and can be spread after natural disasters. Amputation of affected areas or removal of the brain is a potential treatment as well.
What would be cool - well not cool - but there are some bacteria right now that have the ability to pass their antibiotic resistant genes onto other microorganisms that aren't even in their same family, kind of like a bacterium giving another bacterium an infection. Except, that infection actually helps the other bacteria become stronger.
Maybe a MRSA strain gives its resistance to Mucormycosis, and kind of symbiotically hitches a ride on the spores. Then, a series of hurricanes/tornadoes/floods creates a perfect breeding ground for the two microorganisms. As in the answer above, healthy people are usually able to fight off infections, however, susceptible people could be initially infected from the natural disaster fallout. Because the bacteria/fungus duo is super-resistant and less lethal, it spreads quickly as infected peoples' slowly-decaying brains cause them to lash out violently, creating cuts/wounds in others. After the initial natural-disaster-caused infection of susceptible populations, most of the transmission would be from zombie to human, instead of from mud/dirt to human.
I think you'd have to reconcile that the disease wouldn't make the zombies immortal, fast, or super strong. Also, the disease could be spread through infected dirt as well as from a bite.
