Hi,

Deatils:
-Goodman furnace is 14 years old in a 14 year old house
- I live in Canada where we get cold snaps, making the furnace come on more than usual
-when the furnace comes on more often, you'll hear the thermostat click to tell the furnace to come on, the fan will start to run, the blowers light up and it heats the house as normal
-sometimes when the furnace is running, I can hear an intermittent and sometimes ongoing humming which is only heard in 2 rooms, one on top of the other. The humming sound only happens when the burners are on.
-I foil-taped as many joints in exposed ductwork to eliminate air leaks.

I'm not sure what else to do.

In the past, I've replaced the squirrel fan, the main blower motor, the electric igniter etc. so I'm not afraid to DIY. I've never had my furnace cleaned. I got some tools to see into my air ducts from each vent and they all look pretty good.

Any suggestions?

Yes get your furnace cleaned, is it a gas furnace ? I live in eastern Ontario on the lake so don't take chances

Sometimes, heat causes the ductwork or registers to distort and they set up sympathetic vibrations. When you hear the noise, push on the registers and or ductwork where the vibration occurs and see what happens. The vibrations are typically found closest to the heater plenum at this is the hottest section with the most air flow.