Okra, melons, eggplant, armenian cucumbers for vegetables if you want a good harvest.

I'm a bit north of Arizona in las vegas. I came from a colder climate as well. Toucan's suggestions are great for the summer heat but I personally take July and most of August off since I don't really want to garden when it's over 110 degrees. I use the summer heat to solarize my soil in my raised beds to kill weed seeds and most of the unwanted critters that have moved in over the spring. The biggest change moving from a colder climate to the southwest is you can do your best gardening in the winter months. I start cold weather crops in late aug or sept and harvest carrots, lettuce, spinach, peas and other cold weather crops from December to April. I start my summer crops in March and harvest in May/June except for squash which will grow most of the summer as toucan said. I also start seeds indoors over the summer for eggplant, tomatoes and other warm season veggies and plant them out in mid August with some sun protection at first and I get a great fall crop in October. I hope I gave you some insight on your new climate! Experiment and enjoy the longer growing season.

both links specific to our area: 9 things do well in summer

http://cals.arizona.edu/pubs/garden/az1005.pdf

Some other things may last through the summer (annuals that behave like perennials for 2-3 years).

Shade cloth, misters and straw mulch can help. Microirrigation to water 2-3 times a day on automated timer. Deep beds 12-18" deep or in ground to hold moisture and thermal cool.

Here is a link that might be useful: Urban Farm Planting Calender

Here is another big tip: Select varieties that grow to maturity within 70 days. The lower the better. 55 days is perfect but not to many of those. You can have plantings 4 times a year in Phoenix area.

Two usefull links and some great advice, Fascist. I just printed the calander. Thanks for posting them.

A couple of more tips: The best soil for gardening is likely your own soil. People will tell you how terrible AZ soil is but for the most part it is pretty good. You can either plant it and see or get it tested with recommendations from a lab.

You should start a compost pile as well. When a garden annual is spent it comes out and goes either directly into the compost pile or next to it in a drying area (lady bugs and other beneficials often like to make their nests in such debris). Then take a scoop of finished compost and mix into your planting spot before planting your next garden plant. This keeps your garden soil fertile at minimum cost (no fertilizer needed usually).

While the pH of the soil is almost certainly going to be too high the only likely problems with your own soil are salinity and lack of organics. A soil test would identify if those problems are present and make recommendations.

Here is a link that might be useful: Composting