Right/Down/right/Down with an Up/Right/Down thrown in when stuck has worked well for me. My first 1024 block came that way.
When I began playing I was moving around the board in an unorganized fashion, but am now finding that moving the larger numbers to one corner (bottom-right for me) is the best method. By having your block consolidation take place in one particular area, the odds that you'll have matching large numbers goes up dramatically.
I've tried a few games where I do those exact moves with no human judgement and the score ends up quite a bit lower than when I 'generally' follow those moves and consolidate using my best judgement.
Another interesting test was to always play a clockwise or counter-clockwise pattern. The consolidation happens in the middle of the board. This method seemed to result in higher scores than the right/down/right/down pattern.
My new simple algo is:
1. Down until you cannot go down
2. Left
3. Down until you cannot go down
4. Right
5. Go to 1.