Many O(n) algorithms (sorting array with values in fixed range; searching in unsorted array; MST; finding largest binary-search subtree of a tree) are asymptotically optimal simply by virtue of the fact that every element must be looked at at least once.

Also, comparison-search (of a sorted array) is bounded by $\Omega(\log{n})$ for the same reason that comparison-sort is bounded by $\Omega(\log{n!})$

For completeness, O(1) algorithms are also trivially asymptotically-optimal.