If you do want to cancel adventures, here's a few things I've discovered myself.
If it's a multi-step adventure, canceling it has caused me to not be able to complete it ever again. It never reappears on the adventure board. I found this in Egypt with an adventure that took me into a house. I had to leave (I can't remember exactly why) but I could not reenter, so I canceled the adventure. But I have never had the oppurtunity to start it up again, either from the step, or from the beginning.
Also, I had a little trouble with one particular french adventure. I think I had canceled that for some reason (I think because it asked for pomegranates and I had none at the time), then when it popped up again (unlike the egyptian one mentioned above), I picked up some pomegranates at home and went to accept the adventure again on the return trip to France. But this time it asked me for more pomegranates than before! I eventually found that each time the adventure info came up (by clicking on the adventure board enough times to get it), it asked for a different number of pomegranates! So in the end I kept clicking until it asked for the amount of pomegranates I had. lol.
Anyway, maybe that's not helpful, but maybe it is...