I just want to clarify a few points for those currently being scared off ever going in a FJ. This applies to the RAF - the USAF appear to be completely diffeerent.
If you get a pax ride, the limitations are quite stringent (g, rate of climb/descent, no low-level, no ACT etc). Most pilots will fly in a professional manner and, despite what some have said here, the trip is almost always for the benefit of the pax. NOT the pilot. From plenty of experience, there are extremely few (if any) people who could go from no flying experience to a full-up mission without feeling very crap and/or being physically sick. As someone else said, 30-40 mins is about right but as the trip will probably be longer the pilot will normally go on a tour - maybe a PD to the pax's last/next station, maybe see some well known sights from the air - primarily guided by what the pax wants.
Of course none of this means that you cant wind it up a bit - but towards the end of the trip is much better and only if the pax wants to. A pax trip is the time to wind down the testosterone and give someone the trip of a lifetime that they will never forget - for the right reasons.
If you fly on an airtest it is as part of the crew, not as a pax (they aren't allowed on full airtests last time I looked). Groundcrew often qualify under different cateegories than basic pax, so different limitations can be applied, ditto those with an aircrew medical (heavies, helos, holding officers).
For the non-aircrew please do not be put off by some of the posts in this thread - the vast majority of pax pilots (you have to be specifically nominated and qualified) will give you an extremely enjoyable and unforgettable experience. If you ever get a chance, grab it!