The normal usage for 8 bit, 16 bit, 32 bit, 64 bit terminology for cpu's is a reference to the size of the primary registers in a cpu. One exception is the Motorola 68000, called a 16/32 bit cpu because it's registers are 32 bits wide, but it reads and writes memory 16 bits at a time. Intel cpu's didn't use this convention and the number of bits just referred to the primary registers.
The Intel 8080, 8085, and Zilog Z80 are considered 8 bit cpus, because that was the size of their accumulators and most of their registers, although it's program counter was 16 bits, and specific pairs of registers could be combined to form 16 bit values or addresses.
The Intel 8086 and 8088 are considered a 16 bit cpus, but the 8086 accesses memory 16 bits at a time, while the otherwise identical 8088 accesses memory 8 bits at a time. It had 20 bits for addressing memory (so it could support up to 1 MB). The main registers are 16 bits wide, but some of them can be accessed 8 bits at at time (AX can be accessed as AH (high order part) or AL (low order part)).
The Intel 80386 is a 32 bit cpu. The 80386 normally accesses memory 32 bits at a time with a 32 bit addresses. Motorola 68000 16/32 bit processor has 32 bit regisers, but accesses memory 16 bits at a time with a 24 bit address. The Motorola 68020 accessed memory 32 bits at a time. The Intel Pentium Pro is also a 32 bit cpu, but some versions had 36 bits of addressing, that required using address translation schemes.
For a typical PC, the amount of memory that can be read at one time varies with the motherboard and cpu, normally it's 64 bits (called double channel) or 96 bits (called triple channel).
The previous post already posted a link to 64 bit cpus, links to the others:
http://en.wikipedia.org/wiki/8-bit
http://en.wikipedia.org/wiki/16-bit
http://en.wikipedia.org/wiki/32-bit