In Let's Kill Hitler (2011), River Song poisons the Doctor and everyone is certain that he will die. The way he was eventually brought back from death was by River's spending her remaining regenerations... but why would he not simply regenerate on his own?
Two reasons. One we learn during the episode, and one we learn later on.
The particular poison that River uses is identified by the TARDIS voice interface as "the poison of the Judas tree" and notes that "regeneration [is] disabled".
From the transcript:
HOLO-AMELIA: Your system has been contaminated by the poison of the Judas tree. You will be dead in thirty two minutes.
DOCTOR: Okay. So, basically better regenerate, that's what you're saying.
HOLO-AMELIA: Regeneration disabled. You will be dead in thirty two minutes.
DOCTOR: Unless I'm cured, yeah?
HOLO-AMELIA: There is no cure. You will be dead in thirty two minutes.
The Silence knows that the Doctor is a Time Lord; they know he can regenerate. So, if they want to kill him, they would have had to have found something that could bypass his regenerative ability. Presumably, this particular poison has that ability.
(As for why River's regeneration energy works when the Doctor's own wouldn't -- perhaps it's because of the quantity of energy; she gave him all her remaining regenerations in one go. Or maybe it's because the poison is somehow attuned to her bio-energy, which is why she could have it on her lips without killing her, but just the touch of it to the Doctor's lips is enough to contaminate his system.)
But, even more importantly, (and I'm spoilering this since I don't know if you've watched beyond this episode):
The Doctor doesn't have any regenerations left at this point. He may be the 11th Doctor, but he is on his 13th and final incarnation. There is an entire regeneration between the 8th and 9th Doctors that fought in the Time War that refused the name "Doctor" that he doesn't talk about, and the partial regeneration of the 10th Doctor during Journey's End winds up also counting. So it turns out that even a conventional weapon would have killed the Doctor at this point, though he's going to great lengths not to let anyone know that. (Wouldn't you?)