I can't say how much this affects Protoss. Having a unit that can kill Pylons that quickly, is faster than Zealots, and doesn't take the damage bonus from Stalkers looks really hard to deal with. You effectively need Zealots with Charge, which requires 2 buildings after a Gateway plus research. That's a long time to be vulnerable to Reapers.
As a Zerg player, not so much. Oh, don't get me wrong; if you're not expecting them, they will kill off something important. Queens are neither Light nor Armored, so they don't take damage bonuses from much. But a Reaper demolition squad can kill important tech buildings quickly.
I've learned, from online sources, how to deal with Reaper rushes. It's a really simple equation: fast Zerglings + Creep movement = Dead Reapers. Zerglings with speed on Creep move absolutely disgustingly fast. They may as well be ranged units.
Incidentally, I would love to see what Banelings with speed are able to do on creep. I've never really had the opportunity to use them effectively.
Anyway, speed-upgraded Zerglings are the key. So we craft a build order based on getting Zerglings with Speed. Reapers are not a fast unit to get out. A Terran needs to double-Barracks with Tech Labs, so they've got to get some gas. And then they've got to produce a pair of Reapers. If they want speed, they have to put down the Merc compound and research it.
You want to have 3 control open when the Pool finishes. That gives you 1 Zergling pair and (more importantly) a Queen. When the second Overlord finishes, get however many Zerglings you feel comfortable with. When your Queen pops, use Spawn Larva on the Hatchery immediately. However, make sure that when you get 100 gas, you have 100 minerals to get the speed upgrade.
From here, it's just a matter of getting about 10-12 Zerglings, and then paying attention to your base. But of course, that's not all you want. You might want to drop a Creep Tumor (from your Queen) on the Creep, so you can extend the range of your super-speed Zerglings.
You need to make a decision. Since he went for fast Reapers, he's hurt his economy. So you have three choices: break the front with Banelings, break the front with Roaches, or expand. If you choose to expand, make sure that you use the Creep Tumor's ability to extend the Creep to connect your main to your natural. Later, you'll use Nydus Worms, but those are higher tech than you can afford right now.
If you choose to expand, you've basically decided to play a guessing game: you guess what his plans are after his failed harass. Scouting is possible with Overseers. If he goes for air, throw down a Spire and get Corruptors. Indeed, even if he doesn't, Corruptors and Mutalisks together (while very gas intensive) can harass very effectively. If he goes for Marauders, counter with +1 Zerglings. If he keeps going for light infantry, get speed Roaches or Banelings.
Also, one last thing. Creep is your friend. Use Overlords and Creep Tumors to extend the Creep whenever possible. Overlords are a good start, but CTs make permanent Creep. Connecting your bases is good for keeping a fast unit flow between them, pre-Nydus. All of your ground units are substantially better when fighting on Creep.
Note: the above does apply to ZvZ too. Though be aware that if you lose control over a patch of Creep, it can become a highway into your base.