There are lots of zoonoses (diseases transmissible from animals to humans), but most people don't get ill unless they are immunologically impaired. The most common chicken-transmitted disease per the CDC is Salmonella, usually when people handle chickens and then don't wash their hands properly afterwards--but even that doesn't happen too often. So, unless you're immunologically impaired (cancer patient, HIV+, very elderly, child under 2 years old, organ transplant recipient, already battling a serious infection, etc. ) then you will probably be just fine.
There are also warnings from CDC that chickens can be reservoirs for West Nile Virus, but quite frankly even if you personally didn't keep animal carriers for West Nile, any critter within a mile or so of you could carry it anyway--any songbird, any horse, there are lots of carriers for West Nile. So, the best prevention for mosquito-borne diseases is really making sure there's no standing water around your neighborhood for mosquitos to breed. If you have a decorative pond, add goldfish to eat mosquito larvae.
Me personally, I do wear a dust mask or put on my respirator for cleaning the chicken pen, just because getting particles of anything in your lungs--even non-infectious particles like bits of hay chaff or pine bedding--is not good for you either. And the thought of inhaling powdered chicken poo is just, well, icky to me. But, in the interests of full disclosure, I don't always wash my hands after petting the chickens.
Historically, people get more diseases from cattle than from chickens.
