They are an excellent feature for anyone intending to use the live view functions of their DSLRs - which is probably why there aren't too many models with one, since a majority of DSLR users stick with viewfinder most of the time. For those who occasionally use live view but don't have a tilting LCD, they simply don't know what they're missing and so don't make any demands for it.
I have been using DSLRs with tilting screens since my first one 3 years ago, and absolutely want one on all of my cameras if at all possible. Though I am a dedicated OVF shooter most of the time, I find live view plus tilt screen to be invaluable for occasional off-angle shots like down by my feet, through a fence, or overhead...and also for tripod shooting especially at night when doing long exposures.
Nikon had a few models with tilt screen - I don't know if future models will too. Canon has just the one, their first one with it. Sony has long had this feature on many models - going back to the A300/350, and continuing on the A500/550, as well as the new A560/580 and A33/55. Paired with what is truly the least-compromised live view system for regular shooting (full phase-detect AF, no performance degredation or lag, and gain up in main sensor mode for night shooting), I love Sony's DSLR implementation and would recommend those as worth a look for sure.
As far as quality issues - I can't think of any serious issues, having used tilt-screen LCDs on cameras since 1997, and having never suffered a failure of one. I suppose they could be broken if careless...and in some cases they stick out a bit more at the back of the camera which could make viewfinder use uncomfortable for someone with a larger nose or inset eyes. On my A550, the monitor sits almost flush with the viewfinder, so ergonomically, it's something each person needs to try and make sure it works for them - it doesn't hinder my view or comfort at all, being round-faced and small-nosed.