dyld: Library not loaded: @rpath/libswift_stdlib_core.dylib

For me none of the previous solutions worked. We discovered that there is a flag ALWAYS_EMBED_SWIFT_STANDARD_LIBRARIES (in earlier versions: "Embedded Content Contains Swift Code") in the Build Settings that needs to be set to YES. It was NO by default!

This error can occur if something went wrong during the conversion of an Objective-C project to start using Swift. The issue is that the Linker build settings never got configured properly, so you'll have to do it by hand. Look for the Runpath Search Paths build setting and set it to:

$(inherited) @executable_path/Frameworks

EDIT: I should also add that there has been recent spate of these errors caused by something else entirely - Apple made a change in Swift itself, starting in perhaps Xcode 6.1 or 6.1.1. The only solution seems to be to quit Xcode, destroy your certificates in Keychain Access, go to the Member Center and delete all certificates and profiles (except the profiles for apps in the Store - you can't delete them), and then start the entire certificate request process from scratch.

I'm not really sure why this question is being downvoted, I had this problem as well when I first tried to use Swift with an existing project. An Xcode restart also fixed this for me.