My new cat that we've had for about a week has been sleeping with my 6yo in his top bunk. I wasn't sure how she was getting up there. I figured she jumped from somewhere. When I went to get him up this morning I saw her actually climb up the ladder and onto the bed. And she helped me wake DS up. Oh this cat is such a sweetheart. 

The new one hasn't had the opportunity to try it out, but she probably would, too. She's quite the acrobat. 
I did have one cat climb a screen door with his claws and got stuck at the top. He did that a few times actually. 