Why are highly branched alcohols solid?
Well, if you're talking about melting points, the simple argument that more compact molecules should have higher mp because of increased dispersion forces can easily fail.  The problem is that melting is a much more complicated phase transition than boiling, with significant entropic effects coming from considerations of packing and entanglement -- especially relevant for floppy large molecules -- so that arguments based purely on the enthalpic changes due to intermolecular forces can easily be insufficient.