Which elements exhibit allotropy?
Given proper conditions, any element could have multiple allotropes For example, under sufficient pressure, hydrogen has a metallic phase, which may have been observed at Harvard recently.

The extreme example is degenerate matter, formed under the pressure of a collapsed star, though it could be argued that the elements are no longer the same, since nucleons themselves are eventually pooled in a "sea".

If you mean by your question "having allotropes at standard temperature and pressure (STP)", then the list is shorter, of course. Since this depends on the electronic configuration of an element and on the minimal-energy configuration of atomic arrangement, calculation is difficult, but not impossible, and there is software available for crystal structure prediction. 

Now if I could only find a more convenient way to change graphite to diamond, without Superman's help...