Steam instruments:
Plenty of failures, my first vacuum pump pack-up was early during my PPL. Had three and a half more since. On my last one a few weeks ago I flew across half of Europe and back on partial panel. Matter of fact, I don't think I've actually seen a working AH or DI in my last 50 hours.
On the planes I'm currently flying I had the only possible nav failure the other day: a leaking compass (therefore toppled rose). No AH, no DI, no VOR/ADF/GPS, not even a transponder installed, so not many chances of anything going wrong, other than the compass or the map flying out the window.
GPS:
Because of no moving parts, if the electronics are any good (and most of them are) they can withstand a surprising amount of abuse. I haven't personally seen aviation GPS failures as such. The ones I've seen in other environments where mostly due to sheer abuse or in some cases due to design choices which were not appropriate to the environment where the units where being used, mostly weak connectors, bad water/dustproofing, etc.
The most common navigation problems with GPS would appear to be people making wrong entries, database errors or omissions, or general user incompetence, sometimes compounded by bad user interface design. The system works, it just takes you to the wrong place.
So, different systems, different problems. Personally, since I don't fly commercially or for business purposes, I'm not too demanding on my nav requirements. As long as I end up more or less on the right country I'm pleased enough
