Conspire is a keyword ability that allows the spell played to be copied if you tap two untapped creatures that share a color with that spell. Conspire was introduced in Shadowmoor.* By 2010, it was considered a design failure. 
From the Comprehensive Rules
- 702.77. Conspire
- 702.77a Conspire is a keyword that represents two abilities. The first is a static ability that functions while the spell with conspire is on the stack. The second is a triggered ability that functions while the spell with conspire is on the stack. "Conspire" means "As an additional cost to cast this spell, you may tap two untapped creatures you control that each share a color with it" and "When you cast this spell, if its conspire cost was paid, copy it. If the spell has any targets, you may choose new targets for the copy." Paying a spell’s conspire cost follows the rules for paying additional costs in rules 601.2b and 601.2e–g.
- 702.77b If a spell has multiple instances of conspire, each is paid separately and triggers based on its own payment, not any other instance of conspire.
For your reference [CR 409.1b,f-h]
- 409.1b If the spell or ability is modal (uses the phrase “Choose one —” or “[specified player] chooses one —”), the player announces the mode choice. If the player wishes to splice any cards onto the spell, he or she reveals those cards in his or her hand. If the spell or ability has a variable mana cost (indicated by ) or some other variable cost, the player announces the value of that variable at this time. If the spell or ability has alternative, additional, or other special costs (such as buyback, kicker, or convoke costs), the player announces his or her intentions to pay any or all of those costs (see rule 409.1f). You can’t apply two alternative methods of playing or two alternative costs to a single spell or ability. Previously made choices (such as choosing to play a spell with flashback from his or her graveyard or choosing to play a creature with morph face down) may restrict the player’s options when making these choices.
- 409.1f The player determines the total cost of the spell or ability. Usually this is just the mana cost (for spells) or activation cost (for abilities). Some cards list additional or alternative costs in their text, and some effects may increase or reduce the cost to pay. Costs may include paying mana, tapping permanents, sacrificing permanents, discarding cards, and so on. The total cost is the mana cost, activation cost, or alternative cost, plus all cost increases and minus all cost reductions. Once the total cost is determined, it becomes “locked in.” If effects would change the total cost after this time, they have no effect.
- 409.1g If the total cost includes a mana payment, the player then has a chance to play mana abilities (see rule 411, “Playing Mana Abilities”). Mana abilities must be played before costs are paid.
- 409.1h The player pays the total cost in any order. Partial payments are not allowed.
You play Death Bomb, which costs and has an additional cost of sacrificing a creature. You sacrifice Thunderscape Familiar, whose effect makes your black spells cost less to play. Because a spell’s total cost is “locked in” before payments are actually made, you pay , not , even though you’re sacrificing the Familiar.
- If you choose to pay a conspire cost of a multicolored spell, the two creatures you tap don't need to share a color with each other. Each one just needs to share a color with the spell that has conspire.
- You may pay a spell's conspire cost only once. (If a spell has multiple instances of conspire, you may pay each conspire cost only once.)
- A copy created with conspire will have a conspire ability itself. However, since that copy wasn't played, its conspire ability won't trigger. You won't get another copy.
- The copy you create with conspire is separate from the original spell. If either one of them is countered, the other remains on the stack.
- If conspire's triggered ability is countered (by the Scourge spell Stifle, for example), no copy will be created. The original spell will be unaffected.
The latest reminder text for Conspire reads "As you play this spell, you may tap two untapped creatures you control that share a color with it. When you do, copy it and you may choose a new target for the copy."
- Æthertow -
Put target attacking or blocking creature on top of its owner's library.
Conspire (As you cast this spell, you may tap two untapped creatures you control that share a color with it. When you do, copy it and you may choose a new target for the copy.)
There is a total of 11 cards that involve conspire, which divide by color as such:
- Multicolor = 55 %
- Black = 9 %
- Blue = 9 %
- Green = 9 %
- Red = 9 %
- White = 9 %
Creature that grants Conspire