What other road travel services are in usa apart from greyhound?

i wanna travel from new york to ohio

Amtrak train maybe.

Amtrak I believe is the only other way.

You could take a train - that's the only other one I know of other than flying. As an example you can take Amtrak train from New York to Cincinnati for $185 roundtrip. Takes about 18 hours.
Good luck

http://tickets.amtrak.com/itd/amtrak

If by New York you mean New York State, then Lakefront Lines offers service from Buffalo to Cincinnati via Cleveland and Columbus:

http://route.lakefrontlines.com/

Go to Greyhound.com, you might be able to find a route that uses Lakefront lines or some other non-Greyhound carrier (Adirondack trailways?) for as much of the trip as possible, then does greyhound for the rest. Lakefront lines does have better buses with more legroom and movies (although thats a mixed blessing- my last bus movie was "Norbit", yuck).

amtrak or a rental car