There aren't as many zoonotic (transferrable from animal to human) illnesses in frogs as in mammals. Salmonella is spreadable, though most humans w/ healthy immune systems won't get this even when exposed. A well kept enclosure prevents salmonella infection. (If a herp is in a dirty cage, sitting in his own poo, there's a good chance of salmonella spreading.) I think there are a couple of other spreadable diseases (I want to say Giargia, but I think I'm wrong).

If your husbandry practices are good, then your chance of infection -- even with a sick animal -- is greatly decreased. This means:
>washing hands thoroughly with antibacterial soap after handling any animal. (You should was hands beforehand for amphibians, since they are so sensitive to toxins; I'm a smoker and I'm always paranoid about accidentally tarring my frogs to death, so I wash my hands A LOT.)
>Cleaning any and all materials the animal/its gear come in contact with. (i.e. you're cleaning a water bowl. You place it on the kitchen counter. Sanitize the counter. Generally, it's best to avoid animal gear in the kitchen, since that's where your food goes.) I often use vinegar solutions, but if you really wanted to be thorough, bleach solutions are the way to go.
>Ideally, (& especially if you KNOW you have sick animals in your collection), you should have separate gear for each terrarium. (I.e. if you use a hose to drain frog tank #1 for a water change, and frog tank #1 has chytrid or some other contageon, then using that same hose on tank #2 is a good way to spread the contageous disease.)
>A clean tank is much less likely to house/foster disease/bacteria/fungus/parasites than a dirty one. Stay on top of cleaning those cages.

Basically, clean (yourself and your gear) frequently, and just be mindful that the possibility for disease exists, and you and your pets should be fine. (And yes, as someone mentioned in a previous post, you should quarantine new arrivals, just to make sure they're not introducing any new illness to an established tank.)

It should do without saying that you shouldn't kiss pets. Try not to stick pet-coated-fingers into your mouth. Use common sense. (Those adorable baby red-eared sliders were banned because one too many a toddler tried to eat them, and with an infant's immune system, a few got salmonella. Chinatown petstores are not known for good husbandry practices, though.) Frankly, when I was living with someone undergoing chemo (repressed immune system), I kept her away from all reptile gear, just to be overly cautious.

I've had all manner of pets throughout my life, and I've never had an illness that I could attribute to one of my pets. If you try to keep things clean, you and your animals should be fine.