It's my turn, and they have a Bloodline Keeper. I use Brimstone Volley on it. Can they declare a tap and use Keeper's effect to put out a vampire before Keeper gets destroyed?
If the Vampire doesn't have summoning sickness, sure.
If there are restrictions on when you can use an ability, the card will say so . In the absence of anything saying otherwise, the default is that you can activate any ability any time you could cast an instant.
And so people say to me, "How do I know if a word is real?" You know, anyone who's read a children's book knows that love makes things real. If you love a word, use it! That makes it real. Being in the dictionary is an artificial distinction; it doesn't make the word any more real than any other word. If you love a word, it becomes real. --Erin McKean, Redefining the Dictionary
Any activated ability can be used with instant timing ("instant speed" is a somewhat misleading way of putting this, which we generally try to avoid here - instants aren't "faster" than sorceries in any meaningful sense, they can just be played at a wider variety of times), unless it says otherwise, or the rules do. Its cost has absolutely no bearing on this - abilities aren't any different from ones that cost only mana, or ones that involve sacrificing things. They all work the same.
Notable exceptions - abilities that are used with sorcery timing - include Equip and the loyalty abilities of Planeswalkers. Other than that, if an ability is an exception to the usual timing rules, it will explicitly say so.
Jeff Heikkinen DCI Rules Advisor since Dec 25, 2011
How to autocard (do this to specify a card in your posts): Type [c]Black Lotus[/c] to get Black Lotus . Type [c=Black Lotus]The Overpowered One[/c] to get The Overpowered One .
activated abilities can be activated when you have priority unless otherwise stated
activated mana abilities can be activated when you have priority or when you are required to pay a mana cost eg. you can tap your land for mana to pay for the Rings of Brighthearth trigger while it is resolving
MtG Rules Advisor & Goth/Industrial/EBM/Indie/Alternative/80's-Wave DJ DJ Vortex
DCI Certified Rules Advisor from July 14, 2009 to July 14, 2012 DCI #5209514320
Wit found in Rules Q&A
RPJesus: "Man, screw the rules, I'll play a game of 2HG Archenemy Planechase Emperor EDH draft yet. Once I figure out the rules for it..." Chaikov: "Of course, casual Magic may be played any way your Pokemon group agrees on..." and "It's not logic. It's Magic!" GainsBanding: "I only play online. The Magic Online shuffler is AWESOME!" Ikegami: "one might think [adult cats] would make excellent tokens. The issue, though, is that they are very hard to exile. They return to the battlefield more often than an undying creature." Astarael7: "Does 121.1 imply that players are supposed to wear their poison counters?" Bimmerbot: "If you move the wrong way and [the poison counters] fall, it's a game rule violation" Helluminatus: "Just remember, if it looks like a duck, smells like a duck, and quacks like a duck, but the oracle text says creature - Bunny , then by god, it's a bunny." MadCow21: "Who are you and what have you done with the real Chaikov?"