October to September. Seriously. Anna’s Hummingbirds nest as early as mid-October in Tucson, and Violet-crowned and Broad-billed hummingbirds may nest in spring and again during the late summer “monsoon,” fledging young as late as mid-September. No one species nests year round, but Arizona’s 11 breeding species cover 11 months of the year.
Addendum for the rest of the U.S. and Canada: In southern California, where the climate is mild and Anna’s, Allen’s, and Costa’s are year-round residents, active hummingbird nests can be found any month of the year. In coastal central California, with resident Anna’s and migratory Allen’s, the seasonality is similar to Arizona, with a hiatus starting in late summer and lasting until late fall or early winter.
The nesting season shrinks as you go further north, inland, and/or higher in elevation. Anna’s nest from mid-winter to late summer in coastal southwestern British Columbia, but the smaller, migratory Ruby-throated and Rufous hummingbirds don’t even arrive at the northern edges of their ranges until mid to late May, respectively. Exceptionally late northern nests, such as an active Ruby-throated nest in Ontario, Canada in early September (Birds of North America), may represent females taking advantage of abundant late summer resources to get in a third (or even fourth) nesting attempt, while increasingly early arrival and nesting dates are expected in response to climate change.
For more detailed information on hummingbird life cycles, including isochron migration maps for the four most common and widespread species, see A Field Guide to Hummingbirds of North America.