My honda accord backfires from muffler and sometimes the rpm goes down to 1...
 

...while at 60mph. What's wrong? Plus it sometimes dies when traveling far distance.

You did not mention how many miles this Honda has on it. Damn thing sounds completely worn out. The thing until they make aniti-gravity cars that just glide along like flying saucers, the friction will wear them out. The metal keeps wearing and the miles of wiring and tubing and spring-loaded thingies just get weaker and wear and begin to foul up the whole "transportation system." Yeh, your's sounds worn out. Go get you a new one. That one is ready for the crusher.

you should try to check the fuel lines and fuel system coz it sounds that your car engine didnt get a smooth flow of fuel from the gas tank. that is why the RPM goes down while you are running at 60 and it back fires because at that exact timing there are so many fuel in the chamber to be burn and when it goest to the muffler there still planty of unburn fuel and when it goes to the hot muffler, it ignite creating a back fires (just like afterburner in the jet engine) it is cool to watch though but not very economical coz you just wasting a fuel.solution for you, have it check in authorise honda dealer for once a while, if you love your car even if it is old car