Do the search engines know and/or use the amount of traffic your site gets to influence positions?
In theory, yes. In practice, it is almost impossible to say. It also depends what source of traffic you are referring to. All major search engines know what the click through rate is for every result for a particular query. If the SE sees that for the query "blue widgets" item #2 is getting more clicks than item #1, the engine could determine that #2 must be more relevant and move #2 up.
If you are referring to traffic in general, only Google has the resources to track this in any sort of reliable way. There are three ways a search engine can know about your traffic. All major engines use one of these methods, Google uses all three. The first method is tracking hits to ads on pages. This is used by all major search engines, but does not give much useable information, because only a limited number of sites buy ads from that engine, so the SE can't get a valid comparison of traffic. The second method, used by Google, is to get a large segment of the web browsing population to install spyware on their computers that feeds data about every page they visit. There has been some research that indicates it is possible an increase in traffic from Google Toolbar users could cause a small increase in rankings. The third method, also only used by Google, is to offer a web site product to webmasters that sends all your visitor data and statistics directly to the search engine. This has the same limitation as ads in that only some sites will use the technology, however it is possible for the technology to become popular enough the data could be used to influence rankings. There is a theory, for example, that if Google Analytics determines that 90% of searchers who come to your site for a specific term immediately click a link to go to a particular second page, that second page may be moved up in the rankings.
Again, most of this is just theory, but it should give you an idea of what may be possible.
A certain SEO blog did two unscientific tests about a year ago where they got two sets of pages indexed for relatively un-competitive terms, then recruited users to click the pages in different ways. One set of pages was used to test click-thrus on the SERPs - they had readers click only the page in the #3 spot on the SERP page for a specific query, and found in two weeks the page switched with #2. In a similar test, this time using Google Analytics, they found that after a few weeks of simulating a high bounce rate on a landing page the page actually started to slip in the rankings.
They did point out that the changes were slight, on non-competitive terms, and that there was no way to be certain the changes were not due to algorithm tweaks or other factors. I am hunting the link to the study and will post it if I can find it for anyone that is interested.
Before reading replies on this subject of traffic influece on rankings, I was 80% sure that the traffic helped keyword rankings. Now I am 93% sure that it helps rankings.
If you look at SEO after coming to wealthy peace of mind, it really is basic logic. The more we read SEO liturature, the more basic it gets and the more we understand what works for rankings.
Traffic is indeed in the popularity category and probably (93% sure) is included as a criteria for rank. Maybe Google uses Google Analytics to rank sites, who really knows?
So search engines are becoming clones of Alexa?
Of course! traffics affects websites ranking from major search engines. traffics measures how site is established.
I don't think traffic influences rankings yeah clicks in organic ranking may improve the rankings but that also not proven.