I'm not honestly sure I can. I can certainly do merge sort and a really naive quicksort, but bubblesort's not something I've ever written, nor have I even seen a description of the algorithm since my freshmen year of college or earlier. The name isn't exactly descriptive, so if I were asked to implement it I'd probably take my best stab at it and wind up implementing some other O(n^2) sort. Does that make me a bad programmer?

I can do insertion sort off the top of my head, because I find it very intuitive.

Bubble sort always seemed odd to me, and since I can remember insertion sort, if I ever found myself in the odd position of having to write a sort for a program without any reference materials, I'd just use insertion instead.

From looking it up on Wikipedia I found out that I would've remembered it, but it was around 15 years ago that I last wrote one myself. So I would've had to ask if it was the one where you iterate over the values and keep the largest, then repeat. I've learned these at the same time as the other generally known sorting algorithms, so names and details are quite fuzzy.

It probably depends on the position. As a high-level language developer I don't usually implement my own sorting algorithms. Either I use prebuilt libraries that offload work to low-level, or I use builtins, or I ask the database to sort it for me :)