I must still be doing something wrong... when I run the code that agib listed above, I get this:
0x00-0x00: 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00
0x00-0x08: 0x08 0x00 0x00 0x00 0x00 0x00 0x00 0x00
0x00-0x10: 0x10 0x00 0x00 0x00 0x00 0x00 0x00 0x00
0x00-0x18: 0x18 0x00 0x00 0x00 0x00 0x00 0x00 0x00
0x00-0x20: 0x20 0x00 0x00 0x00 0x00 0x00 0x00 0x00
and so on, down to 0x08-0xF8. I get the same results with two different chips, which is why I think something isn't right. One of them is a brand new engineering sample, delivered from Taiwan earlier this week. The other was removed from a device (motorcycle dash) that was produced in 2003.
I'm using a Sparkfun Wee, attached to an FTID TTL-232R cable. I've got pins A0, A1, A2, and Vss on the EEPROM wired to GND on the Wee, Vcc wired to 3.3V, WP jumpered over to Vcc (which should enable WP), SCL to pin 5, and SDA to pin 4.