I have big squares of festive fabric that i have hemmed, i wrap them around presents as i would paper then tie ribbon around them.
I have also made drawstring bags of varying sizes for the same purpose.
I have bags/wrappings for both birthdays and Christmas, my friends like seeing the same fabric come out and so does the 7yo.
I have been doing this for about 4 years now, ever since i saw the Japanese scarf tying stuff on MN.
However, i don't wrap gifts in fabric/bags if they're being posted (various customs will often rip them open to check dodgy contents), or for other people's children. I will use fabric where i know i will get it back.
I have stashes of stuff going back years, from family and friends (1960s curtains, 1970s bedcovers, 80s kids stuff, off-cuts from the market etc). Theyvall look really jolly under the Christmas tree.
This year i may also make some little 3D folded bags out of felt - i'm up to my eyebrows in felt!