I"m a wrapping procrastinator. In years that I'm very organized I start and finish on the 23rd. More typically it's the 24th, and many years I'm still wrapping a few on the 25th!
When our kids were young and getting lots of gifts, there were often too many for me to stash away from them, plus they wanted to see gifts under the tree in the days before Christmas. I didn't want to identify which gift was for whom because the temptation to sneak a peek would have been too great for them, so I put little notes to myself about which gift was what.
For instance, when they were in their early teens if they looked at six different gifts jumbled together under the tree they might have seen 183, 175. 153, 171, 154. and 166. The games began for them to figure out the method to my madness.
My code represented the number of letters in the last names of each of their first grade teachers (hubby included - I found out her name from my MIL). 183 identified it as being for my son Garrett. His 1st grade teacher was Mrs. Williams, and it was the third gift I wanted him to open.
Another year I added up the hour and minutes of their births and used that. So 4:53 am was 4+5+3 meaning I put 125 (5th gift to open) on that package. Most years one of my kids would crack the code a couple of days before Christmas. It kept them very busy and they greatly looked forward to the game. They started off working individually but would eventually collaborate. Being the first to crack the code meant major kudos, and the solution was kept secret until all had solved it.
That morphed to me putting very cryptic notes/hints on the gifts. One year I didn't bother and the hoohah and disappointment over the lack of notes made me realize how much my family looked forward to them. So I brought it back. (For instance, the note on a box of warm slippers might say, "Excellent for toasting but not good much for eating.")
I mostly use wrapping paper unless something is such a weird size and shape that it doesn't lend itself well to that. Birthday, shower and other during-the-year gifts usually go in gift bags, but Christmas presents are nearly always wrapped.