I read:
"5 Golden Rules" - a book that covers 5 important-ish theorems and their proofs, from Game Theory to Geometry.
"What is Mathematics?" - a general book the goes into enough depth to be satisfying.
Having read those, a few topics interested me enough to read further.
"A Topological Aperitif" - A really wonderful, short book with great illustrations, assumes little, a nice introduction into Topology.
"Elementary Number Theory" - Quite good - lots of worked examples meant I felt confident about using techniques that I'd learnt from the book.
"Principles of Mathematical Analysis" - Pretty terse at points, but I found it interesting. My interviewers were impressed by this choice also, commenting that it was a first year undergrad text, and continued to quiz me about it, just to check that I wasn't lying!
But don't read for the sake of a personal statement - read because you are genuinely interested! I also browsed through books like "Gamma" (a constant that was 'discovered' by Euler, but is somewhat less famous than 'e') and a few books about graph theory, which wasn't really my cup of tea - just read what takes your fancy. To be honest, I think that they don't care especially about how much reading you have done - they really just want to see if you can think logically, quickly, accurately, and perhaps laterally!!