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.