Popular average-case complexity assumptions

Except for planted clique and random 3SAT, what are the other commonly used average-case complexity assumptions?

Often times average case complexity is used in the study of data structures for upper bounds (eg., of hash tables), but there are also some useful lower bounds. For example, the worst case $\Omega(n \log n)$ lower bound on sorting can be generalized to the average case, and to randomized algorithms as well (eg., see these lecture notes)