The game was a two-player board game where both players try to make it to the "Regeneration Zone" to become "the next Doctor", although it confusingly also stated that you've both started glowing, and several events which can happen to the player make little sense under its framing, such as regenerating into multiple forms in spite of there being "only enough regeneration energy for one of you to change".
For the purposes of this list, a "regeneration story" is one in which a regeneration is actually and initially depicted. For this reason The War Games is not included below, even though it is commonly thought of as a "regeneration story". It doesn't actually include a clear scene of regeneration, and the preponderance of stories in other media confirms that the Second Doctor did not regenerate at the end of it.
Additionally, immediate post-regeneration stories, like the 2005 Children in Need Special Born Again — and ones like Castrovalva, where the regeneration sequence was replayed — are not included.