I've got a board I'm working on that I think may have two USB ports and both of them could conceivably be connected to a computer at the same time. Both USB connectors need not be connected to the PC, but I'd like the board to be powered by USB from the PC when one or both of them is plugged in. Can I simply connect the 5V pins on both USB connectors together on my board to achieve this outcome? It's all the same 5V net on the PC internally anyway, right? If you don't think it's sound to connect 5V to 5V on different USB connectors, then please propose an alternative solution.
I think it's fine, and I'd just connect them.
However, if you want to be extra safe, note that some USB voltages can be quite a bit lower than others, due primarily to the drops in the current limiting devices in each hub. Or you could invent even stranger cases, like having one plugged into the end of a chain of bus-powered hubs, and the other plugged directly into a self-powered hub. Shorting the +5V signals together may end up causing current to flow backwards in some of the hubs, if one device's voltage is higher than the other. Active electronics, like hubs that support power switching, may be damaged by that.
Instead, you can connect each +5V through a diode to your +V rail on your circuit. Your circuit's +V would be dropped a bit (maybe 0.6V for a 1N4148 or similar diode), but the USBTiny and FT232R should likely both be OK with that.
Since your needs are for a USB serial converter and a custom embedded programmer, one very attractive solution could be to choose a slightly more capable USB microcontroller and implement both the custom programmer and USB-serial conversion in it. This will likely be more cost effective and save board space/complexity.
The virtual com port type of converter has gained a lot of popularity over the last few years, there is reference code for most USB micros.
A simple means of combination would be to have an input which puts the software in one mode or the other.
Another possibility would be to run the programmer off of the USB serial, or even get a dual USB-serial chip and use one channel of it.
If they are going to the same set of USB ports on a computer, it should be fine.
If however, one is going to an onboard USB port and one is going to a USB hub, there may be a difference in voltage between them that can cause problems.
If there is any chance each port could be going to different computers, it could really cause problems, as the two computers might not be at the same ground potential and you are connecting their power supplies to each other.