You can also save the TripIt itinerary from their web site as a PDF and then email it to yourself. Open it on the phone and open in iBooks or some other PDF app (iBooks doesn't let you annotate PDFs but otherwise is very good for storing PDFs).

Actually, I like the Kayak trips better, in part because TripIt has removed some functionality, like embedding screen shots and pics into your itinerary and being able to print it. Kayak Trips will send you notifications of any changes to flights without you having to upgrade to a Pro version like TripIt.