This operation is often called sequencing, and is available in the standard libraries of some functional languages (such as Haskell). In Scala you can either implement your own, or use an external library like Scalaz. Suppose we have the following, for example:
val xs: List[Either[String, Int]] = List(Right(1), Right(2))
val ys: List[Either[String, Int]] = List(Right(1), Left("1st!"), Left("2nd!"))
Now we can write (using Scalaz 7):
scala> import scalaz._, Scalaz._
import scalaz._
import Scalaz._
scala> xs.sequenceU
res0: Either[String,List[Int]] = Right(List(1, 2))
scala> ys.sequenceU
res1: Either[String,List[Int]] = Left(1st!)
As desired.
As a side note, this operation just requires that the outside container be traversable and that the inside container be an applicative functor. Scalaz also provides a ValidationNEL class that's a lot like Either and also fits these requirements, but using sequence on a list of ValidationNELs collects multiple errors instead of stopping at the first:
val zs: List[ValidationNEL[String, Int]] =
List(1.successNel, "1st".failNel, "2nd".failNel)
Now we get:
scala> print(zs.sequenceU)
Failure(NonEmptyList(1st, 2nd))
You could also use sequence on a list of Options, Promises, etc.