Hi there Rocko ! You can certainly try anything, so long as you are prepared to not get a heavy crop [or in fact, possibly not gain a crop at all.] The biggest factor is when is your earliest possible frost date. If it is less than three to four months away, then there is a good chance certain plants will not make it to maturity before being killed by an early frost. You can still try to grow whatever you want, and see how it does.
If you pick specific plants and varieties, you still have plenty of time for a nice fall garden. Like I said, a lot depends on when the first frost happens in your area.
I doubt melons or cucumbers will do well planted this late. For some suggestions on late summer/fall gardens, see this site :