I know that it is possible to enter Burma/Myanmar from several border crossing with neighbouring countries, and I'm pretty sure that from some of them at least you do not have to be on a package tour.
But I have been unable despite much searching to find out for sure whether it's possibly to enter Burma from a border crossing with one country and exit via a border crossing with a different country?
If so, which countries and which border crossings would this be possible at?
The same page on Wikitravel as referenced in Zeocrash's answer continues:
As of March 2007, travel beyond Kengtung to the rest of Myanmar is not possible, even with a valid tourist visa
Kengtung is a town several hours by bus from the Thai border. We stayed there for a few days and then took a domestic flight to Inle Lake. You can also fly to Mandalay and Rangoon and continue to the accessible rest of the country from there.
I did meet people in Burma who crossed the border from China but that involved a pseudo tour with a $200 price tag.
I also know someone who left Burma into Thailand overland from Rangoon, but I do not remember which border crossing she used.
I myself entered in Mae Sai and flew out of Rangoon to Chang Mai, which means it is possible to use different crossings when entering and exiting.
If the question is whether you can enter from one country and exit into a third, this seems possible from China into Thailand as long as you have the required permits to visit usually off-limit areas.
Unless you try super hard and have very good connections it seems not possible to cross the Indian-Burmese border which is what many people including me would love to do.
it seems that it's very dificult to enter Burma by land, legally. As for illegally, well burmese prisons aren't particularly nice.
Hopping across the Thai border into Myanmar's border towns is easy, but crossing into or out of Myanmar proper by land varies between difficult and impossible. Visa-free entry is possible at some border crossings, but you must then exit Myanmar via the same border crossing, usually (but not always) on the same day that you enter, and fees apply (normally US$10). All land border crossings into Myanmar give only restricted access to the border areas. The only way to visit locations throughout the country, is to enter and exit Myanmar by air.
taken from: wikitravel - entering burma by land
For those who enter from one border and depart from another border point to a different country, it is possible in Tachileik-Mae Sai, Thailand border and Muse-Shwe Li, China border (vice versa).
