Can life exist on any of the recently discovered planets that orbit other stars?
We sure hope so! The search for life is an exciting motivator that gets us to find new planets, build new telescopes and study their atmospheres. We have only one example of life on a planet in the Universe. One way to search for life on other planets is to look for their effect on the atmosphere - does it produce oxygen and methane the way life on the Earth does? If it has a solid surface, liquid water and atmosphere like the Earth, it could be a sign of Earth-like life. There is a big focus on planets that are in the so-called habitable zone - the location where an Earth-like planet is not too hot and not too cold so it can have liquid water, a requirement for all life we know of.
There is a growing list of planets that are in the Habitable Zone, one catalog is here:
Of course we don't know yet if any of these planets host life, nor even if they have a solid surface or an ocean. Sometime in the future, we may be able to measure these properties and also to look for bio-signatures (such as methane and oxygen) in there atmosphere. This list should just keep growing and including more and more Earth-like planets.
UPDATED by Everett Schlawin, July 18, 2015