I recently saw a mix up of all of the Doctors regeneration scenes.
When the second Doctor changes to the third (from Patrick Troughton to Jon Pertwee in "The War Games, Part Ten" (1969)), it is forced on him as punishment before being exiled to earth. The Doctor was not critically injured or dying. The transformation was the Time Lords doing.
Does this really count as one of the 12 regenerations?
There is no indication in Old Who or the New Series that regeneration is exclusively limited to being uncontrollably triggered by fatal events.
Although regeneration is usually seen in the show as an "emergency fail-safe" feature, we're also shown very explicitly that most Time Lords choose to regenerate for reasons other than imminent death. Romana is the most prominent example, although Borusa also comes to mind (the man seems to have gone through bodies like some people go through ties).
The Doctor just leads such a hard life that his regenerations come more violently than most Time Lords'.
The fact that it was forced on him by the Time Lords doesn't change anything either; the High Council has repeatedly been shown to have control over the regeneration technology (for example, offering the Master a new set of regenerations if he helped them in The Five Doctors). There's no reason to assume that the process they used to change the Second Doctor into the Third was not regeneration; in fact, their dialogue in that scene makes it clear that the process is identical to that which turned the First into the Second (though "regeneration" wasn't yet really a term being used by the show).
Yes, it was a regeneration. However, the way Romana casually "tries out" different appearances suggests that the emergency regeneration that happens when a time lord "dies" is a completely different kind of thing than the one forced on the Doctor. Unless Romana actually intended to shorten her life span to about half, that is.
Yep, it was his first regeneration
