There's not a lot of research information about passion flower's medical effects.
It's a beautiful flower though! I would encourage having some in your garden if possible.
Here's a reference to a 2007 Cochrane review:
Passion flower is mentioned in a good 2006 review article on complementary medicines in psychiatry, from The British Journal of Psychiatry:
Here's a reference to a 2001 study from Iran, showing that passionflower relieved anxiety to a similar degree as oxazepam (a benzodiazepine), over a 4 week trial.
The same author published a study suggesting that passionflower could help with opiate withdrawal symptoms:
In conclusion, not a lot of evidence. The existing studies are only of short duration. But passionflower extract does look like an interesting substance to research further.