While I don't mind them, they are still a rather inferior and 'failed' storage medium.
At the time of the PSPs release they were cheaper than the memory carts like the DS used...but that quickly changed and thus the UMD became another betamax. While they offer a good amount of space, they are fragile and the disks do not have any sort of protection on them (physical kind). Just another attempt of Sony trying to push a new format on the industry, and while it holds a ton of space (1.8gigs), it was a rather fruitless attempt.
Quite frankly I am happy that Sony will be switching to another physical medium with the PSP2, most likely those pro duo cards we use or something close to the DS but with more space.
I take damn good care of my UMD collection, but I certainly wont miss em in the next generation.
EDIT: Although I hope to god that the PSP2 will have some sort of backwards compatibility with PSP1 games. They can keep to UMD drive in for that, or sell a UMD drive add on for all I care. Hell maybe even have a legit way of ripping our PSP1 games to digital form. I just want friggen backward compatibility.