A couple resources that might be of use:
If you subscribe to it (annoyingly, I cannot get at my copy), the American Academy of Pediatric's Red Book may contain incidence figures. I don't recall, but it contains a remarkable amount of information in it.
For viral diseases, most if not all entries in Fields Virology have an Epidemiology section, and many of these touch on the incidence rate, especially for more common diseases.
In addition to the CDC (listed in another answer), take a look at the Agency for Healthcare Quality Research (AHRQ)'s Healthcare Cost and Utilization Project (HCUP) data. While this will only give you incidence in terms of hospitalizations rather than all cases, it may be potentially useful.
Beyond that, I'd suggest looking for particular papers, or search for "DISEASE OF INTEREST" meta-analysis in Google Scholar or PubMed for overall incidence figures.
Additionally, a useful formula:
Prevalence = Incidence * Duration. Which in turn means Prevalence/Duration = Incidence. If you can find those two pieces of information, you can calculate the incidence for what you want.
There's also a way to extract incidence from a mathematical modeling paper about a disease which reports an R0 figure, but that may be a touch technical given your stated desires.
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