[Snaidis]

Who has greater basicity? Furan, Pyrrole, Pyridine or Oxazole?
My thoughts: pyridine is the first because his electrons does not participate in aromaticity, and the conjugate acid is pretty stable. Next is oxazole, almost the same reason, but the oxygen is more electronegative, so it taken electrons inductively from nitrogen. Next is furan who has a lone pair which does not participate in aromaticity, and the last one is pyrrole which all his pairs participate in aromaticity.
What do you think? Thanks!

[SadBloke]

To sum up, you rank them Pyridine, oxazole, furan, pyrrole.

I think that sounds reasonable. You can verify by checking the pK_a of Pyridine and oxazole, which will tell you which is a stronger base. Pyrrole seems to actually be an acid, so I think it should be last. I'm not too sure about furan but I think that a neutral O, in general, is a mediocre base so it makes sense that furan would come after pyridine and oxazole (both of which contain basic N). So, I think you got it.

This is a handy chart for some heterocyclic pK_as:
http://www.scripps.edu/baran/heterocycles/Essentials1-2009.pdf