I was lucky enough to be on the flight deck for half an hour or so during a flight from LHR to LAX on a Virgin Atlantic A340.
Gorgeous view of Greenland with dotted cumulus around.
However that was pre 9/11, end of April 2000 to be precise.
The best flight deck rides have been pushback to shutdown with Ryanair (around ten times) and Mearsk (pre arranged with the Captain of the flight - a round trip to Milan).
Unfortunately it seems that if you are flying, at least, with a British and American airline then your chances are nil.
As for other airlines... not sure. I have heard Air France allow it but this is unconfirmed.
The way I used to do it was to ask the cabin crew as I boarded, handing them my licence, logbook and explaining that I was a PPL, I am studying for my ATPLs and would it be possible to visit the flight deck at some point during the flight. The Ryanair cabin crew always took me straight to the flight deck and asked the flight crew - within a couple of minutes I was strapped in being shown the emergency escapes, oxygen mask location and use, the overhead panel for the jumpseat radio point (listen only, no transmit). Once the captain was eating his crew meal (apple) flyign out of Dublin and handed his kneeboard to me saying, "Do you know the ATIS frequency for Cardiff?" "Yes its 128.82." (I fly from Cardiff Airport myself). He dialled it in and asked me to write it down for him (the Captain was PNF that sector).
Then it all changed for the worse in the matter of a few hours. I was sat at this desk typing on this same keyboard at work when it was happening. Never forget that day.
Best wishes,
Charlie Zulu.