I do too. We don't have a lot of different varieties around here, so I am always happy to be able to identify a new bird in the neighborhood.
The jay is called a Mexican Scrub Jay. They are similar to the Florida Scrub Jay, but are found here in the west. My two jays are a mated pair and very tame. They will take peanuts out of my hand. They nested in the backyard this spring and I loved watching them take care of their babies. I am very attached to my jays, although they really are very mean birds - nest robbers and bullies in the neighborhood....but I love mine anyway. I've been feeding this pair for years here. I can't go out in the backyard without them following me around demanding their peanuts.
You know what birds I just love? They are so friendly and I’ve had strange ones land right on my shoulder while out in the woods. The little Chickadees. Do you have them where you are?