If you get your hands pooey and then the poo gets transferred to your mouth or food, then sure, you can get intestinally ill, but the solution of course (as with any other animal) is Don't Do That
As SpottedCrow says, wash yer hands after playing with the chickens and you should be fine.
The bacteria that cause some sorts of abscesses in chickens (as in other animals) can do the same in humans, so if you are doctoring a bird with an abscess, practice good sanitation. In particular, don't be poking at oozy abscesses with bare fingers if you've got a cut or scrape on your hand. Pretty much common sense.
If your chickens should get mites, the mites may crawl on your arms etc when you work in the coop, but although it may feel weird and annoying, they will not actually "live on" you (they won't set up an infestation of your home or whatever) and it just lets you know it's time to get more serious about getting rid of them from your chickens
Oh, and don't be breathing lots and lots of dust (esp. not chronically) from a funky old coop, as it can install bad germs in your lungs.
That is pretty much all I can think of offhand that you have any
realistic chance of catching from your chickens.
Good luck,
Pat