Как проверить, существует ли файл в папке Documents?

Swift 3:

let documentsURL = try! FileManager().url(for: .documentDirectory,
                                          in: .userDomainMask,
                                          appropriateFor: nil,
                                          create: true)

... gives you a file URL of the documents directory. The following checks if there's a file named foo.html:

let fooURL = documentsURL.appendingPathComponent("foo.html")
let fileExists = FileManager().fileExists(atPath: fooURL.path)

Objective-C:

NSString* documentsPath = NSSearchPathForDirectoriesInDomains(NSDocumentDirectory, NSUserDomainMask, YES)[0];

NSString* foofile = [documentsPath stringByAppendingPathComponent:@"foo.html"];
BOOL fileExists = [[NSFileManager defaultManager] fileExistsAtPath:foofile];