Andy_Langton - 2:25 pm on May 11, 2012 (gmt 0)
The easy answer is that it depends. For some keywords Wikipedia is a safe "default" choice, since the content is almost always reasonably good, and searchers seem happy with Wikipedia in Google results. In these instances, Wikipedia and similar sites are quite easy to beat.
In other areas, Wikipedia has very strong articles with large numbers of links into them, and can be very stiff competition.
In terms of assessing organic competition levels, you should look at both on-page factors (allintitle: is a good starting point) and off-page - is Wikipedia's page ranking purely because it has internal links to it? If so, then it would usually be supplanted easily by a page with good external references and links.