Can I run my furnace in fan-only mode without a G wire?
I would make the assumption that the furnace and fan wires are "bonded" together somewhere between your thermostat and your control board, therefore sending 24vAC to both relays and turning both on.

I'm assuming you don't have AC since you don't mention it, so in this circumstance you're probably looking at needing four wires -- ground (C), fan on, furnace on, and a positive feeder (R) (to power the thermostat and to send back to the relays).

To make the house more future-proof, I'd run more wires than needed in the event AC is ever added or the system changes configuration.

I have casual knowledge of HVAC, but in my experience of designing microcontroller-based thermostats, this is generally a good idea.