...using an iterative procedure (no hash table)?
It's not homework. And by mode I mean the most frequent number (statistical mode). I don't want to use a hash table because I want to know how it can be done iteratively.
OK Fantius, how bout this?
Sort the list with a RadixSort (BucketSort) algorithm (technically O(N) time; the numbers must be integers). Start at the first element, remember its value and start a count at 1. Iterate through the list, incrementing the count, until you reach a different value. If the count for that value is higher than the current high count, remember that value and count as the mode. If you get a tie with the high count, remember both (or all) numbers.
... yeah, yeah, the RadixSort is not an in-place sort, and thus involves something you could call a hashtable (a collection of collections indexed by the current digit). However, the hashtable is used to sort, not to calculate the mode.
I'm going to say that on an unsorted list, it would be impossible to compute the mode in linear time without involving a hashtable SOMEWHERE. On a sorted list, the second half of this algorithm works by just keeping track of the current max count.