My Dad was over from New York for a couple of days at the start of the week and being thrifty, although now very well-off, he stayed with us (no hotel room required) ! We didn't see much of him as he left early and came back late to do business in London but I was able to give him his birthday present to take back with him and save money on international postage.
The present was frugally wrapped in a free tourist map which shows the area he lives in. It was much more personal than buying wrapping paper and cost nothing other than remembering to save it the last time we were over.
I never buy wrapping paper unless it is very cheap at a jumble sale. Alternatives include maps as detailed above, tissue paper which comes as packaging in other things, ironing paper from gifts you have been given, free paper which comes as part of charity appeals and printing fancy papers free from the internet. You can also use cloth and tie it in fancy ways as they do in Japan.
I also always save pretty packaging. For instance, 5 Christmases ago when my Mum was still alive she gave everyone's gifts in huge gift bags. They have been re-used every Christmas since and now I think it is becoming a bit of a tradition and is a nice way to still think of my Mum at the festive season.
What do you do about wrapping paper ?