The hardware we have installed Jira ranged from a 1 Gigabyte VM with 8 Gigabytes of Hard disk, up to a 2 CPU Dual core server.
90% of the time with mySql as the backend, 10% of the time with HSQL
Operating System has been whatever the LTS variant of Ubuntu, or the more up to date version of RHEL (or CentOS as the case might be)
JRE has always been the most recent version from Sun. We only use fisheye and Crucible internal to our company, but that accounts for 60% of my experience.
In the last four years (and 10 or so versions) - I've never had a random failure or null pointer cause a failure. It's been the most reliable software package I've ever used.
Interesting that we have two completely polar opposite experiences.