Everyone likes a vampire now and then, and each time my players figure out what they are facing and he goes down to Deadly, they immediately launch into the "I'm cutting off his head with my katana/spurs/combat axe, etc".

Now I know SR is notoriously abstract with many things and that is fine, my players always seem a little miffed when they have an unconcious-regenerating thing at their feet, yet can't seem to cut off it's head at point-blank range. This isn't really a problem as much as I am curious how you others handle this.

I pretty much give them the called-shot bonus of staging-up the wound level, and let them make a skill test (2) since most of the penalties offset. This usually forces the target to makes a few more 1d6 rolls vs. death and rarely does the beast go down during the first round of decapitation attempts.

My initial dealing with regeneraters, I'd let each PC generated 2 successes over Deadly "bump the 1d6 roll" up a level. For example, 4 additional "over-deadly" successes would mean the baddy would need to beat 3d6 instead of 1d6. Since then, I've just reverted back to the original 1d6 in the interest of canon.

What other ways have you all handled regeneration?

well, the longest a regenerating creature is going to stay down and unmoving is three seconds, minus however long it took to get him to D damage. it should be hard to get in a proper decapitation within that short a time period. i think the current rules work fine, for that.

personally, though, i think regeneration should automatically heal (Essence/6) boxes of physical or stun damage per turn, starting with stun. as it is, it's too all-or-nothing for my tastes (especially for a playable race).

I've gone with 2nd edition rules

I hate what 3rd edition did with PC shapeshifters. In general, I think I'd allow the characters to make some basic skill check, then let the downed vampire try to soak the damage (remember why the guillotine was invented. Even a strong executioner might take a few whacks to take that head off, and until you sever the spine, the vampire can still heal and get up again).

If they do Serious damage with an attack, they severed the spine. His neck starts healing, but he's paralyzed. Gives 'em a chance to finish him off.

How long does it take to execute a coup de gras. (SP?) And, are there specific rules for delivering a mortal strike as a complex action? (no books here)

I like the "over deadly", it's nice option. One of my players started carrying a mono-whip to make it just that much quicker. Just wrap it 'round the neck and pull.
A couple of tricks that could give your regens time to get back up:
1)minions. so much fun right there
2) magic, specifically anchored spells like barrier that pops up when they go down. Don'y knw if it's always the case, but people that become vaamps often develop magical skills.
3)armor, like a helm or gorget. or quickened armor spell.
4) turn to mist before they get to deadly, go regen somewhere and attack again.

The one time my group got to face a regenerator, it was the serial killer from Prime Runners (the possessed ork in Detroit). The guy nearly took out the entire party - they just kept filling him with lead until he stayed down.

Even a really strong character can't get up if he has a metric ton of lead in his system.

only in that they get the critter to D more quickly.

my understanding of the regen power is that any projectiles are expelled from the body as it regens, so having an ass load of bullets in your corpse isnt too likely, although a couple Hvy machine guns on a vamp would at least hinder his movement....alittle.

it does say that cybernetic implants are expelled from the body. i'd imagine bullets would be, as well, though it doesn't actually state that as far as i remember.

I seem to remember that too, but I don't see it in the Critters book (p.13-14) and no reference in SR3 so I am not sure where else would be a SR3 point of reference beyond these sources.

i think it's in the shapeshifter section in the SR3Comp.