Ecuador is great for hitchhiking, just be careful in some places, especially at the coast. Many pick-up trucks are there. Drivers might ask for money, but if you can explain your situation you will get away with it. Many Ecuadorians are happy to pick up a foreigner. It's not the safest country to hitchhike though.
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Along the Panamericana there are several Toll-Stations ("Peaje"). Take a Overland-Bus in direction of your destination and get out at the first Toll-Station (normally 0,25cts - 0,50cts). You have a couple of seconds to ask the other drivers until you get kicked out by the police, but that's normally enough time to find a ride. If you are able to explain your situation in Spanish, you might be able to stay longer. If you want to avoid this kind of "trouble" you can as well try to stop cars along the Panamericana. Along this road normally you won't get asked for money.
Buses in Ecuador are quite cheap (usually 1$/h), and will usually stop anywhere. On some roads, though, there are no buses at all, in which case hitchhiking can be a good alternative, and you will be most likely picked up quickly as well, tough it is more difficult to find a free ride on small roads. Very often the very first car that passes will pick you up.