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it would depend on what you would like to sort/resources available etc..

heapsort O(n*log(n)) and it is in place

but the most practical one is quicksort: worst case O(n*n), average O(n*log(n)). It is in place and the costant factor is very small

i think it's merge sort because its complexity is O(n*log(n)) and we need O(n+m) time to merge two sorted vectors

I think Bubble Sort is the best! Teaches you to be patient. Go Bubble!

Seriously: this is an idiotic question. It all depends on the context, i.e there is no best which works everytime.

ABCsort is blazing fast (O(n), and never moves records or keys); its output is an index table of pointers to records. The algorithm is patented by the author, however, who sells examples. It runs about 3* as fast as QuickerSort for 30-character records, for example, and is even faster when implemented in Field Programmable Gate Array HW. Check out my writeup via any search on 'ABCsort'. And oh, yes: sorting on multiple keys at once works nicely on a multiprocessor like a Sparc.

quick sort is the best sorting method.