I just replaced an old Honeywell mercury thermostat with these series of letters and numbers on the inside: HB2 T222A 1012 1 with a new RTH2300. There were 3 wires in the old thermostat, red connecting to R, white connecting to W, and a green wire connecting to B. Where do I put the green wire in the new thermostat?

If you have a forced air furnace either gas or electric the Green wire is for the fan and should connect to G, however check the manual in the following link as there are exceptions.

http://customer.honeywell.com/techlit/pdf/PackedLit/69-2327ES.pdf

Please note on page 7 number 6 there is a JP1 switch that needs the correct position if wire G is used.
Hope this helps.