Yeah, I can't imagine an entity in a real project even with more than 100 columns. Its rare case. But if you entities (rows/tuples) of some class (table) can contains variable set of columns (properties) you can look at hstore contrib module.
Is there are hard limit of 1600 that you cannot get around?
Yes.
Generally, wanting more than a few dozen columns is a good sign that you need to rethink your schema design. What are you trying to accomplish exactly?
indeed. I'd say a good read on 'data normalization' and the Third Normal Form would be in order.
relational databases are *not* spreadsheets (and, for that matter, spreadsheets make lousy relational databases)
if these 1600+ elements come from an ORM, you probably need to rethink your object model, as no sane object class should have that many members.