Definitely I carry a copy of my e-tickets. Perhaps domestic I don't, but international flying I do.
I also now make a point of noting all the addresses of where I am staying (hotel or friends'/relatives' residences), as well as hotel confirmation printouts.
I've been pulled up on a number of occasions where having e-tix copies was required:
- Checking in for a long routing at BNE I with QF, the lady made me show e-tix for ongoing flight plus ask a question as to where I was going after my final destination on the itinerary.
- Travelling back to LON from MUC I was stopped in the airbridge and asked for my passport. They then asked me to show where I was going after LON, with e-tix as proof. Actually, the e-tix copy I had with me was for the wrong dates (it was my original dated booking which I had later changed to an earlier date). But when I explained it seem to pass mustard.
- To enter MNL airport (i.e. to actually step through the entrance doors to the building), you need to show proof that you have a booking.
- Philippine passport control have asked me before if I have a continuing / return journey ticket, to which I replied yes and then they asked me for proof.
List goes on a bit, but enough to convince me that I need to carry copies of my tickets.
I know some people get away with showing electronic copies or TripIt details, but in some cases this may not be possible (no connection, use of devices is against the rules, not good enough proof, etc.)