What do great programmers know that average programmers don't?

Well both the average and great programmers somehow knows the solution to the problem. But the difference is how the problem should be solved in a smarter way in terms of usability.

REQUIREMENTS.... Great programer "Listen, Gather, Understand and Acknowledge" the requirements carefully before start coding.

Average programmer code can only add "extra" cpu cycles!!

This is very broad question. There is so much that "great" professionals know in general compared to the average.

• Experience. Time in the market, delivering many different kinds of software, in many different contexts with many different teammates, for a long time, makes a lot of difference. No theoretical training can replace what a good amount of real problem solving and practicing can match. The key is not doing the same things for a long time, that amounts for nothing. People that hold too strong to his current skill set, not wanting to learn something new, are usually weak
• Experimentation and practice: programmers that only code in work hours specifically for the job requirements are not practicing enough. Expose oneself in open source projects, both by directly collaborating and also just watching and tinkering do a lot of difference.

The question is very generic

Sometimes every person thinks him/her self a professional,,,,

All the times, you need to think that there is somebody better than you.... So you can become better.

There is a web developer and there is a senior developer and there is a development lead, and there is a development manager or project manager.

Think about it and know each one of these.

Know yourself...!!!

profesional programers know the short road to fix a problem and their code is more dynamic and more flexible than avarage programers.

The difference is flexibility, way of thinking the problem, and profesional and clean code

Thats'a secret.. I cant tell that openly. :)

Experience. Time in the market, delivering many different kinds of software, in many different contexts with many different teammates, for a long time, makes a lot of difference. No theoretical training can replace what a good amount of real problem solving and practicing can match. The key is not doing the same things for a long time, that amounts for nothing. People that hold too strong to his current skill set, not wanting to learn something new, are usually weak.

Great programmers work smart whereas average programmers work hard...simple.

Answer is different for different skill levels. I will try to categorize,Beginner: Linked List, Stack, Queue, Binary Search Tree. Intermediate: Heap, Priority Queue, Huffman Tree, Union Find, Tries, Hash Table, Tree Map.Proficient: Segment Tree, Binary Indexed Tree, Suffix Array, Sparse Table, Lowest Common Ancestor, Range Tree.Expert: Suffix Automaton, Suffix Tree, Heavy-Light Decomposition, Treap, Aho-Corasick, K-d tree, Link-Cut Tree, Splay Tree, Palindromic Tree, Rope,  Dancing Links, Radix Tree, Dynamic Suffix Array.I have seen all of the listed data structures being used in various programming contests.Many of them are given in language libraries. But it is very important to understand their dynamics. Otherwise understanding related higher level structures will be difficult (if possible).One may find some higher level data structures easier than lowers.

The programmers should know the logic if they have capability to visualize the required output then it will be easy to write code. this skill will be able to get through experience only.