As far as paperwork goes, before I set out on a trip, I do the following:
1. Passport - scan the key pages into the computer as a pdf and ensure that my parents have that accessible somewhere in case I need it sent to me. Then I also photocopy those pages - I carry a copy with me and I give a copy to my parents. Of course, I bring the original with me.
2. Other Identification - same as with the passport - scans and photocopies. I bring a copy and the original with me. This would include driver's licence, provincial health card, etc.
3. Financial - I make sure both my parents and I have got the phone number for my credit card company, and any additional information which might be useful if my financial stuff were stolen.
4. Travel Insurance - scan the insurance papers into the computer as pdfs and ensure my parents have a copy. Photocopy those pages - bring one with me as a spare copy, and give one copy to my parents. I also bring the original with me.
5. Bicycle - same as above with the receipt and bicycle insurance information ... except that I don't bring the original receipt with me.
6. Transportation Info - because I make most of my transportation arrangements online, I just forward the confirmation emails on to my parents so they have it all. Then I print out two or three copies of it all - two to bring with me, and one to give to my parents. This information would include: flights out and back, trains, busses, car rentals, etc.
7. Accommodations Info - I rarely book all my accommodations, but if I do book some, I will do the same as above with whatever I have so that my parents and I have copies of it all. I will also ensure that my parents have the email address to Hostelling International, in case I need something looked up or to give them a place to start looking for me if necessary. In addition to that, I will bring my Hostelling International book, and I will occasionally print out a bit of accommodation information- maybe options for a particular city or something.
8. Itinerary - I make sure my parents know my basic itinerary. They might not know the exact details, and in fact I might not know the exact details, but at least they have an idea of where I'm heading.
9. Phone Numbers and Addresses - I've got several index cards with all the phone numbers, addresses, and email addresses of family and friends both back at home, and where I'm heading.
10. As I mentioned I either carry two copies of most of the stuff above, or the originals and one copy with me. I keep them in different places on the bicycle.