I've got flash carts for my 2600 (Harmony), NES (PowerPak), SNES (Super Everdrive), Genesis/MD (Everdrive MD), SMS (Master Everdrive), and PCE (Turbo Everdrive). For a few cases I have my flash carts acting as the entire library since I usually need money and space for other things. But in most cases they supplement my collection as opposed to replacing whole libraries.
I think flash carts are great on a "try before you buy" basis and help give me a much better idea of how a game plays than trying it out in emulation. And in that way they've helped me be smarter about what games I pick up, so that way I don't buy a game, wind up not liking it, and then flip it around shortly after. I also find that flash carts are fantastic for parties and meetups since I don't have to drag a whole bunch of carts along if I'm getting a console set up.