The 150 in 1 originally mentioned by Howard has crept down to about $6 shipped for a Famicom version. I bit.
EDIT - another thing I noticed is that we are in the era of single game reproduction cartridges. Roughly $15-30 each for both rare retail games and weird fan projects (like FF VII NES). Clearly someone is able to reprogram these PCBs....
There are points on the pcb that make me think that a proprietary McGuffin is placed over the pcb and they are flashed that way. Unfortunately I'm not a hardware guy that can look at a chip and tell what point is for what, so I'm not sure how to re-flash them.
As yots said, re-flashable eproms make things simpler. If you are willing to manually flash the game you want to play via a pc connection, you can make a generic cart on most systems at this point. Some cavets apply, like nes roms needing the proper mapper from a donor cart, ect....
I'm looking at the 70's style stuff and thinking that a bank switching cart might be the way to go. You can easily fit 90% of the 2600 library on a couple of eeproms. Vectrex, colecovision and ect are the same way. (note to self: purchase vectrex).
I saw a Spanish site where a guy had used a cheap avr and had up/down buttons that changed the game number, displayed on 7 segment lcds, instead of dip switches for one of these 2600 multi carts. I'm wondering how much more kit/expense it would take to have a cheap lcd just display the game label instead.