Obviously this depends a lot on your stack: Node.js is going to be your best bet though. Sinatra + Unicorn can drive some pretty nice reqs/second, but if what you need is actual "concurrency" as opposed to just reqs/second performance, go Node. Express benchmarks that I ran a few months ago were showing ~7k requests per second, and I've heard claims of well over 10k.
Depending on your scale, your DB could be another potential bottleneck. Heroku provides hosted PostgreSQL DB's as a standalone service, and their performance has served me well in the past; could be worth looking into for you. Also, of course there's the Mongo in the room: I've heard mixed reviews, and I've never employed it in production myself so I have no wisdom to impart regarding it. Just be aware of your options :)
Depending on your scale, your DB could be another potential bottleneck. Heroku provides hosted PostgreSQL DB's as a standalone service, and their performance has served me well in the past; could be worth looking into for you. Also, of course there's the Mongo in the room: I've heard mixed reviews, and I've never employed it in production myself so I have no wisdom to impart regarding it. Just be aware of your options :)