Virtually any plants that grow an appropriate size and enjoy the sun conditions you describe can grow in a window box. However, you must take care to provide some extra things. Basically, a window box is a pot. So, like a pot, you must provide DRAINAGE; all nourishment: I add Osmocote to a high quality potting MIX (not soil) at planting; liquid fertilizer twice a month; and most of the water: daily in the hot summer months, less in spring and fall, depending on your weather.
It's a good idea to think about the design before you shop and plant. You want something tall (12-18 inches) and showy: zinnias, marigolds, geraniums, miniature boxwoods, bulbs, come to mind immediately. Then you want something that is soft (filler): Euphorbia diamond frost, diascia, Lobelia, carex, for example, and then you want something that will spill over the sides: boston ivy, petunias, scaevola, lantana, sweet potato vine, calibrochoa.

Look at magazines, keep your eyes open at parks, theme parks, and office complexes, anywhere there are good looking pots. You can get lots of great ideas that way.

I just threw these DW begonias in these tiny window boxes on my shed and was very happy with the result.

Sorry, forgot to attach the pic!

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Have had success with the pink or red Begonia semperflorens and a vining Dichondra 'Silver Falls.' Sometimes I tuck in a white alyssum. The latter sometimes flakes out in mid-summer but picks up again in cooler, late summer-fall weather.