My favorite means of travel is bike touring. Generally defined as long distance rides, ranging from a day to months, even years. I love it because there's no barrier between you and your environment. It's just you and the open road. You're senses become sharp and you begin to pick up on the subtle stories told by your surroundings.
If for whatever reason you don't fancy many miles on a bike, I've found that ground transportation is the next best option. That's basically, trains, buses, shared taxis, and boats of some kind. To be clear, this perspective is coming from a budget minded traveler who had a lot of time, but I still think everyone should do an international road trip if they want to truly understand a country or region.
Don't believe me? Think about a tourist coming to the US for a visit. They fly into NYC, take a short flight to Boston, then fly to L.A. where they'll end their trip. That's such a fraction of what the US represents. Traveling by ground allows you to see the capitals, the mid-size cities, the small towns, and the country side. It allows you to have a deeper understanding for the soul of the country and its culture. If you just take a flight from mega city to mega city you miss a lot of that.
I traveled by bus my entire journey in South America, from Buenos Aries, Argentina to Medellin, Colombia. Here's some pictures and a video from a small portion of that trip I took from Salta, Argentina to San Pedro de Atacama. Enjoy the views!