In this work we ask the fundamental question: How many bits of information can be stored in a crossbar switching network? The answer is trivial when the switches of the network are in series with diodes (semi-conductive) but it is complicated when the switches are regular contacts. Exact explicit expressions and simple asymptotic bounds of the storage capacity (in bits) are derived for the general crossbar switching network with regular contact switches. Categories and Subject Descriptors B.3 [Memory Structures]: Misc.; H.0 [Information Systems] General Terms Design, Measurement, Performance, Theory. Keywords Capacity, Crossbar, Device, Information, Memory, Network, Nanotechnology, Nanotube, Nanowire, Storage, Switching.