You may be able to achieve really high rankings for obscure terms that no one is likely to search for but realistically you are unlikely to get a number one spot for a popular keyword or phrase.
Realistically very few people apart from those looking for their own site will go past the first three pages and so with much lower rankings are not going to be seen very often and it wont make a great difference whether your site is listed on page ten on page one hundred million and ten. It therefore makes sense to target keywords and phrases where you at least have a reasonable chance of getting into the first few pages.
One unusual thing that you may notice once you are finally able to get listings high enough to find is that your same page may have different rankings each time that you look at it. Often you find that your ranking jumps back and forward between two completely different values. This doesn't mean that Google is promoting your site to a higher rank then dropping it back, promoting it again etc. What it means is that Google is in the process of moving your site from one position to the other and hasn't finished the move yet.
Google runs on many different servers around the world and exactly which one returns the results that you are seeing will vary as the load is shared between these different servers.
I don't expect that Google would ever get all of their servers synchronized to display the same results all the time as by the time the last server is updated to reflect one lot of rankings the next round of changes will have started and the first server will be showing new results. Of course if your site is going to rank the same in the new list then your position in the search results may stabilize but as everyone is competing for that coveted number one spot in the search results for their selected search terms you can't expect things to stay static for long especially if you are targetting popular terms.
The only way to do your search on a specific Google server each time is if you specify the IP address of the server rather than the domain name "google.com" which is shared between all of them. Of course there are sites out there that have discovered several of these IP addresses and have set up a page that displays the results of the same search on different Google servers in iframes on the same page. The Google Data Centers Analysis Tool for example provides this comparison between 17 Google servers on the same page.
This article written by Stephen Chapman, Felgall Pty Ltd.