Correlations between two likert-type scaled items (i.e., discrete ordered variables) are called polychoric correlations. You get an excellent guide here (the site also suggests programs for estimating the correlations):
http://www.john-uebersax.com/stat/tetra.htm
The basic idea of polychoric correlations is that the discrete ordered variables are manifestations of underlying continuous variables. Thus, the polychoric correlation (under certain assumptions about the underlying variables) reflects the correlation you are interested in (i.e., the correlation between the underlying continuous variables).
In Stata, -polychoric- is user-written command, which is excellent for running polychoric correlations. Download the command to Stata by entering -findit polychoric- into the Command window.
/Kristian