I was just reading this article about allotropes which relates allotropy with some specific elements and also this wiki article. Also some other articles some of which relate allotropy with catenation some with electronegativity and some with electronic configuration. I was understanding the relation of allotropy with all these factors but I am unable to get that how allotropy is dependent on them exactly. Can we predict the allotropy in elements (and also the extent to which they exhibit allotropy) just by concerning their chemical properties?
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...