Since Swift 4.1 you can use compactMap:

let possibles:[Int?] = [nil, 1, 2, 3, nil, nil, 4, 5]
let actuals = possibles.compactMap { $0 }

(Swift 4.1 replaced some overloads of flatMap with compactmap. If you are interested in more detail on this then see for example: https://useyourloaf.com/blog/replacing-flatmap-with-compactmap/ )

With Swift 2 b1, you can simply do

let possibles:[Int?] = [nil, 1, 2, 3, nil, nil, 4, 5]
let actuals = possibles.flatMap { $0 }

For earlier versions, you can shim this with the following extension:

extension Array {
    func flatMap<U>(transform: Element -> U?) -> [U] {
        var result = [U]()
        result.reserveCapacity(self.count)
        for item in map(transform) {
            if let item = item {
                result.append(item)
            }
        }
        return result
    }
}

One caveat (which is also true for Swift 2) is that you might need to explicitly type the return value of the transform:

let actuals = ["a", "1"].flatMap { str -> Int? in
    if let int = str.toInt() {
        return int
    } else {
        return nil
    }
}
assert(actuals == [1])

For more info, see http://airspeedvelocity.net/2015/07/23/changes-to-the-swift-standard-library-in-2-0-betas-2-5/