Are there any plants that fix their own nitrogen?
There are no known plants that fix their own nitrogen. However, there soon may be!

Because N is the major limiting factor in agricultural productivity, there is huge interest in plant systems which can fix their own. It's important enough that the Bill &amp; Melinda Gates foundation have started a project aimed at reducing dependence on fertilisers by giving plants the ability to fix their own nitrogen. There are several potential strategies, the most obvious being encouraging more species to form symbioses with nitrogen fixing bacteria.

However, there's another proposal which builds on recent discoveries about the mechanism of nitrogen fixing in bacteria: we now know how the crucial enzyme complex is made (Rubio &amp; Ludden, 2008). As a result, there are many people calling for efforts to engineer the system directly into a plant organelle (e.g. Beatty &amp; Good, 2011; Godfray et al., 2010).

So, in 10-15 years time you can check back and the answer to this question might have changed! The most likely answer then will be "just the usual suspects: rice, maize, wheat".

References:


Beatty, P.H. &amp; Good, A.G. (2011) Future Prospects for Cereals That Fix Nitrogen. Science. [Online] 333 (6041), 416 –417. Available from: doi:10.1126/science.1209467 [Accessed: 2 February 2012].
Godfray, H.C.J., Beddington, J.R., Crute, I.R., Haddad, L., Lawrence, D., Muir, J.F., Pretty, J., Robinson, S., Thomas, S.M. &amp; Toulmin, C. (2010) Food Security: The Challenge of Feeding 9 Billion People. Science. [Online] 327 (5967), 812 –818. Available from: doi:10.1126/science.1185383 [Accessed: 2 February 2012].
Rubio, L.M. &amp; Ludden, P.W. (2008) Biosynthesis of the Iron-Molybdenum Cofactor of Nitrogenase. Annual Review of Microbiology. [Online] 62 (1), 93–111. Available from: doi:10.1146/annurev.micro.62.081307.162737 [Accessed: 2 February 2012].