Grappling and pinning an opponent makes it much easier to hit them; but, a grappled opponent is not considered helpless. You can not coup de grace an opponent who is grappled or pinned. (See the Condition Summary, DMG pp. 300-301). Note the penalties that each of these conditions apply:
Grappling: Engaged in wrestling or some other form of hand-to-hand
struggle with one or more attackers. A
grappling character can undertake only
a limited number of actions. He does
not threaten any squares, and loses
his Dexterity bonus to AC (if any)
against opponents he isn't grappling.
Pinned: Held immobile (but not helpless) in a grapple.
From the PHB (p. 153):
A helpless opponent is someone who is bound, sleeping, paralyzed, unconscious, or otherwise at your mercy.
If you're engaged in the grapple, or pinning an opponent, you can strike the opponent using a light weapon, or deal unarmed damage. Binding a character takes 1 minute (per the Use Rope skill, PHB p. 86); but, it would render the character helpless.
As a DM, I might override the rule and say that another character standing could maybe coup de grace a character pinned by an ally, depending on the circumstances. Strictly by the book, though, it's not allowed; the rules are quite explicit, on this point.
There aren't rules for strangling in the PHB; I would suggest using a grapple check each round in conjunction with the Suffocation rules (DMG p. 304)
Another suggestion which could be used as a house rule: Spycraft has the concept of "mooks", who are the disposable, non-plot-critical NPCs that are often gunned down quickly in movie gunfights, or beat up in droves by kung fu masters. If you were trying to "neck snap" a mook-type NPC, the DM could opt to use the Spycraft rules.
When a mook takes damage, the mook gets a damage save against the number of points of damage taken. (I think it would use the character's Fortitude save bonus?) If the mook fails the save, the mook instantly dies (or is knocked unconscious). As the mook continues to survive and take damage the save DC is cumulative; so if the mook takes 12 damage, then 9 damage, his first save would be at DC 12, and his second save at DC 21.
Again, it would be up to the DM to decide if it's appropriate to borrow this rule.
I just discovered that there ARE rules for execution in Book of Vile Darkness (p.39):
The condemned must first be secured by being tied in place, pinned in a grapple, or successfully restrained in a stationary execution device. If restrained in an execution device, the condemned can make a[n] Escape Artist check every round.... If grappled, the condemned can attempt to break the grapple normally.
Once the victim is secure... The executioner makes a Profession (executioner) check against the DC given.... If the check is successful, the condemned is slain.... If the executioner fails, the execution is botched, and the executioner can make another check the following round.
For a Headsman's Axe, the Execution DC is 18, and a botched attempt results in a Coupe de Grace. Using this rule, it's possible to have one or more characters pin an opponent in a grapple, and have another PC perform the execution (using a headsman's axe). It's up to your DM whether he wants to allow this in his games... and whether he wants to allow other weapons to be used.