It is a fact that thieves go inside the busses to snatch small bags in whatever way it can succeed. For instance when some passengers fall asleep.
You have to keep an eye on your daypack all the time. Also in restaurants, if you put it on another chair or even on the back of your own chair, for instance.
I've witnessed all of this personnally (not particularly in Ecuador). But they have never succeeded with me.

Joolz, this tactic has been well-documented on several forums. It's easy for us to say "I did such-and-such and never had a problem" --I say it myself, actually--but the fact remains that it does happen. Despite others' warnings not to put stuff on the overhead, I did that myself all the time, and "never had a problem."

We just returned from a one week trip to Quito, Ecuador. We walked and took public transport everywhere without any problems. The govt. seems to be aware of all of the concerns mentioned in this thread and is on a campaign to change the image of the city. We noticed that in the tourist areas (Zona Mariscal and Zona Centro Historico) additional lighting is being installed on many streets and there are police officers everywhere, nearly on every corner. And I am pleased to say that they were the friendly kind that like to chat and give directions, not the scary type with shotguns. From what I could gather much of the theft takes place in the bar districts as drunk or stoned tourists are an easy mark. For ordinary tourists I would say be cautious, but not worried.