Visualizing large posets

John Stembridge's site containing Maple packages for symmetric functions, posets, root systems, and finite Coxeter groups could be helpful.

David Cook, Sonja Mapes and I have a package for Macaulay 2 which draws pictures of posets, either with or without node labels. It will produce the TikZ code to include these in papers as well.

How large though is "very large"? While there are a number of built-in enumerators in our package (lcm lattices, hyperplane arrangement lattices, noncrossing partition lattices, etc.) which can produce fairly large posets quickly, the only limitation might be how you're storing or inputting these posets.

I feel certain that Ziegler's Fig. 2.1 below (to which I assume you are referring?) was just drawn "by hand" in a generic drawing program, such as Adobe Illustrator, or xfig.
          
           _{(p.643 = 27th page of notes linked by Camilo)}

This is probably not what you want, but Mathematica (via Combinatorica) can draw Hasse diagrams. See, e.g., this link for how to accomplish this.