Travel Insurance
Backpack being investigated by a horse, hopefully covered by travel insurance for Ecuador!
Buy travel insurance: Travel documents for trip preparation.
Travel in Ecuador, on horseback in the mountains, requires medical insurance
Backpacker with travel insurance in Ecuador
Hiking in Ecuador - with trip insurance, of course!
Volunteer with travel insurance, in Ecuador
Volunteer doing conservation work in a forest in Ecuador, hopefully with the best travel insurance!
Ecuador travel insurance
is a sensible precaution.  Buy suitable trip insurance for your situation, e.g. volunteer, backpacker or existing medical conditions.

Travel Insurance

Buy travel insurance for Ecuador before you leave your home country - most insurers will refuse to provide a travel policy starting after you have left.  Your trip insurance should also cover the cost of your Ecuador flights if you are unable to travel, so it is worth buying a policy as soon as you book your flight.  The insurance cover you require will depend on your personal situation. 
The best travel insurance is different for every traveller, but is rarely the one offered by the travel agent.  Compare travel insurance online to get a good overview of what cover is available at what price, and remember that the best insurance is not necessarily the cheapest.  It may be a false economy to buy cheap travel insurance if it leaves you without the cover you need, but if you're prepared to reduce cover for minor ailments or lost luggage, or accept a higher excess, you may be able to bring down the cost of your policy.
Worldwide annual travel insurance may be a more economic option than a policy for each trip if you travel often, but be aware that there is often a limit to the length of each trip, perhaps 30 days.  If your Ecuador trip spans more than a month or so, a backpacker travel insurance policy may be your only option anyway.
Travel Medical Insurance
Ecuador is a developing country with limited medical facilities.  Good travel medical insurance, i.e. a policy including evacuation by air to a country with better hospital facilities if necessary, could be seen as sensible.  This is even more important for older travellers or those with existing medical conditions.  Young, healthy travellers who speak fluent Spanish might prefer to take a cheaper travel insurance policy with a higher excess and see a local doctor for any minor health issues, but you'll still need travel cover in case of serious illness or emergency.  Those with existing worldwide health insurance may not necessarily be covered for travelling in Ecuador - check your policy carefully.  Remember that the travel health insurance policies offered as part of a bank account package, etc., are often not valid worldwide, or for trips of more than 31 days, so do check.
Personal Belongings Insurance
The risk of pickpocketing is significant on public buses and crowded markets.  However, if you don't carry anything of high value when you travel, then the amounts involved may be lower than the insurance policy excess.  If you have an expensive camera and your high-end travel gear cost a small fortune, the situation would be different.
A comprehensive worldwide travel insurance policy with a high level of personal belongings cover and a low excess might be an attractive option if you have a lot of high-value items in your luggage.  Check the cover limits on individual items.
Backpacker insurance policies with medical and liability cover but no baggage insurance are cheaper.  You will save money on the insurance premium, if you can accept that you may have to spend some of the savings in replacing a few of your belongings.  This can be good value for experienced travellers with low-value luggage, but do make sure you have adequate cover for medical emergencies or legal situations.
Sporting Activities Cover
Extreme sports enthusiasts should buy a trip insurance policy which covers their specific activities in Ecuador.  You might have to pay an extra premium for cover for some activities, especially riskier adventure sports such as mountaineering or diving, but even tranquil outdoor pursuits such as hiking or snorkelling sometimes require special sports cover.
Volunteer Travel Insurance
Some insurers class volunteering or internships as work, even if you are not paid.  Buy a suitable travel insurance policy, make your insurer aware that you will be an intern or volunteer in Ecuador and check that the tasks involved in your volunteering are not excluded from cover.
Insurance for Older Travellers
Travel insurance for those aged over 65 is not so easy to find and for those over 75 it is even more of a challenge.  If you are UK-based, Saga claim to have no upper age limit for their travel insurance policy.  Remember to search for travel insurance to cover existing medical conditions and declare those conditions when signing up.  Unfortunately, cheap insurance does not really exist for older travellers, it's more a case of finding the best travel insurance policy at the time.
Travel thoughtfully in Ecuador - be aware of your surroundings, keep hold of your valuables, don't flash expensive possessions around, don't allow yourself to be distracted and don't take your eyes off your luggage.  Here's hoping that, like many visitors, you'll have a peaceful visit to Ecuador and won't need to claim on your travel insurance. 
Travel insurance plans vary, you must choose a policy to meet your specific needs.  Before you buy trip insurance, shop around and perhaps even use an insurance comparison site to get the travel cover you want.  Only you know how prone you are to illness, accidents or losing things.  Your choice of hotels and transport also affects the risk of loss.  For trips of more than 31 days you will find rather fewer choices available and a backpacker policy might be your only travel insurance option.

Travel Insurance Ecuador
Travel insurance - trip insurance policy options for Ecuador, travel medical insurance, levels of cover, backpacker travel insurance policies vs. comprehensive cover, travel insurance for volunteers, interns and older travellers.  The best travel insurance? Tips for buying trip insurance.  Note that no responsibility can be taken for the content of external links or for reliance on any of the suggestions on this site.