We are looking to go to South America this winter. My wife and I have three boys. Age 17, 13 and 12. We are an athletic and active family looking for an activity based time away. Looking for a safe country to travel in with a unique culture to experience. Any suggestions?

South America is at present quite stable, and I wouldn't be concerned about taking kids to any country. Within some countries, there may be specific areas best avoided. Although I've only been to one, I imagine each country has its own uniqueness.

So - active holidays. The only part of South America I've been to so far is Ecuador, and there's tons of opportunity there...I would certainly recommend it. We did a one-day biking tour, but the same company, Biking Dutchman, does tours up to eight days which would no doubt be lots of fun (Tip - if you bring your own pedals, as some people on our tour did, also bring a pedal wrench...for some reason they don't have one.). We also encountered some other travelers who had done a rafting trip in the Andes, and of course there's also trekking and horseback riding opportunities. There's many ecolodges both in the Andes and in the Jungle that make good bases for those sorts of things. Along the coastal regions and in the Galapagos, you can also do snorkelling, diving, etc.

If you mean your winter our summer, then I would suggest you look into both the lake district and Patagonia in Chile and Argentina. There would be endless opportunities for outdoor activities and views of glaciers, penguins, and volcanoes. The are is covered with different national parks on both sides of the Andes. January and February are high season, so you need to plan a bit regarding lodging and flights.

Ecuador is a good country to travel with family in South America. It will be a good adventure holiday. This adventure holiday can be enjoyed by foot traveling, horseback and also mountain bike. It is having many distinct habitats,from high snow-capped volcanoes and Amazonian rain forest to tropical beaches and the unique Galapagos Islands. Combined, these very different landscape types create a country with one of the greatest varieties of flora and fauna on Earth.Ecuador is also one of the most volcanically active parts of the world and the country’s most important mountains are all volcanoes. With its lush equatorial rain forest, together with a host of spectacular mountains, Ecuador offers almost endless possibilities for the adventurous family.

Suitable for children age 8 and over:-
Traveling involves a mix of trekking and touring along with optional activities such as pony trekking, mountain biking etc. During traveling you will experience a variety of climates from the dry, cold air at 5000 meters (16,400 feet) on Cotopaxi, to the hot and humid Amazon Rain Forest.

I may not be the best judge, since we've only been to one South American country, but we spent 2 weeks in Peru last summer and loved it. (By "we" I mean 2 parents and a then 10-year old.) We divided our time as follows:

- Lima, visiting friends. We saw a circus (a Cirque de Soleil-type circus with acrobats, no animals), which is apparently a pretty common thing to do. We liked the museums, Spanish colonial architecture, and food.
- Puerto Maldonado and Amazon rain forest. Really cool! We stayed in an eco-lodge, saw some animals and birds (and heard even more that we couldn't see amongst the dense leaves), and learned from a medicine man. We went out on a boat early one morning for a fishing trip, and our son caught a piranha.
- Cuzco and Machu Picchu, naturally. Pretty amazing. We could have spent hours there, but our son got tired of walking around. He enjoyed the hot springs in Aguas Calientes afterwards, though. We did some hiking but did not do the Inca Trail; we took the train there.
- Puno and Lake Titicaca. We saw the floating islands and had lunch with a local family. We chose not to go kayaking, but that is an option if you want to be more active than we were.

Argentina is one more amazing place to visit in South America with family. Traveling with your family in Argentina, you can lounge on warm ocean beaches, ride a train to the end of the world, ski or hike in the Andes, visit one of the wonders of the world, Iguazu Falls, or watch enormous ice blocks drop into the Arctic Ocean at the tip of Patagonia.

All the suggestions above are good.
Since it'll be summer in the southern part of South America, it'd be a good opportunity to visit Patagonia.
Other places/countries you might consider - Bolivia, Peru. They have all you can imagine - ancient and colonial architecture, indigenous and European culture, spectacular mountains and jungle, the biggest salt desert in the world, hot springs and geysers.
If you like outdoors there are lots of opportunities - trekking in varied terrain, mountain biking, whitewater rafting. You can easily buy all those tours with local tour operators.

I thought I'd comment on Jayson77's post.

in Argentina, you can lounge on warm ocean beaches, ride a train to the end of the world, ski or hike in the Andes

There are really no beaches to speak of in Argentina. The closest beach in Buenos Aires is in Uruguay, across Mar del Plata.
There are no trains in Argentina, apart from a few short connections around BA.
There is no skiing in summer season (January). Hiking however is a good idea for that time of the year.