I started assembling links but then realized that Wikipedia is a good starting point, it has provides a nice summary of all the most notable designs: tethers, bolas, orbital rings, pneumatic towers, the Lofstrom Loop... Each has its own drawbacks, but the important thing is that they do not require nonexistent (even if theoretically possible) materials.

Clever ways to get to space are often covered at Next Big Future, including the author's own nuclear cannon proposal - this one actually literally follows Jules Verne :-)