If you have a memory-constrained system, yes. There's a surprising amount of stuff that sits untouched in RAM for very long periods of time. I generally run fairly low-end systems, so it's not unusual for me to have a few GB in swap. (Though I just found out last week that I could buy another 4GB for $26 and free shipping, and I have to admit that was a worthwhile investment.)
Yes, if you have 8GB of RAM which is enough for me 99% of the time, but you'd rather your computer slow down 1% of the time rather than crash and have to start over.
But is hibernate relevant? I've found suspend to be much more reliable, and good enough in terms of energy consumption (thanks to modern low-power states in CPUs).
I find it relevant. I use it to store the state my work laptop is in at the end of the day, and then restore that state when I get back to work the next work day. That way I don't need to keep it switched on when I'm not using it/transporting it.
Is there a better solution to this other than hibernating?