For an idea of the most common ones:
Linear:
Like a single iteration over list .
O(nLog(n))
Incredibly common. It’s the Time Complexity of any algorithm that takes any input, splits it in 2 pieces and solves each piece recursively. EG Merge Sort. Another reason it’s so common is because it’s the time complexity of any algorithm who’s most expensive step is the sorting of the input.
O(Log(n))
This happens when algorithm is doing a constant amount of work to throw away a constant fraction of the input. EG Famously Binary Search Algorithm.