There are tour agencies and private hire companies in most cities in Ecuador which can provide a car and driver to take you on a local sightseeing day trip or a long distance journey. You can also rent a car or van to transfer to an airport, consulate or a more remote location.
For the most part, when you hire a vehicle, the driver will only speak Spanish. If you want an English speaker it may be better to go through a tour agency and ask for a guide who can provide more information on the route and will know good places to stop. A driver might just take you to his copadre´s restaurant.
If you don´t mind sharing you can also use a van service to travel between the main towns and cities. More services are appearing as people are prepared to pay a little more due to doubts about the safety and security on buses.
A few things to note: 1. If a van is full it might actually be more uncomfortable than a bus. 2. Some services are more direct than others. Check the route and journey time and also that it´s not a courier service. 3. There is often a luggage limit. 4. Vans will take you to their office. If you want to go directly to your hotel you should advise the driver in advance and pay a few dollars extra.