It depends on the child's developmental stage. I got both my boys one of those little cars they sit and scoot on (about $20) on their first birthdays, but my daughter is delayed so I got her a tent thing with a bunch of balls in it ($30 Walmart.com). So much fun! I also push the books, board books with feel and touch is great for little guys and Dr. Seuss too but I don't suggest the board books as they cut out some of the story. Anything sensory.
There is a wide variety of toys available for 1 year olds but I have always been the type of person who likes to give something that will grow with the child. Maybe a walking toy that then becomes a riding toy when the baby is a little older. My 'go to' gift is always books - get one that is is made for babies to chew on or has different textures they can touch but then get a nice book for the parent to read to the child. Green Eggs and Ham is a great choice just because the rhyming sequences are entertaining for any age child.