Any way to replace characters on Swift String?

You can use this:

let s = "This is my string"
let modified = s.replace(" ", withString:"+")    

If you add this extension method anywhere in your code:

extension String
{
    func replace(target: String, withString: String) -> String
    {
       return self.stringByReplacingOccurrencesOfString(target, withString: withString, options: NSStringCompareOptions.LiteralSearch, range: nil)
    }
}

Swift 3:

extension String
{
    func replace(target: String, withString: String) -> String
    {
        return self.replacingOccurrences(of: target, with: withString, options: NSString.CompareOptions.literal, range: nil)
    }
}

This answer has been updated for Swift 4 & 5. If you're still using Swift 1, 2 or 3 see the revision history.

You have a couple of options. You can do as @jaumard suggested and use replacingOccurrences()

let aString = "This is my string"
let newString = aString.replacingOccurrences(of: " ", with: "+", options: .literal, range: nil)

And as noted by @cprcrack below, the options and range parameters are optional, so if you don't want to specify string comparison options or a range to do the replacement within, you only need the following.

let aString = "This is my string"
let newString = aString.replacingOccurrences(of: " ", with: "+")

Or, if the data is in a specific format like this, where you're just replacing separation characters, you can use components() to break the string into and array, and then you can use the join() function to put them back to together with a specified separator.

let toArray = aString.components(separatedBy: " ")
let backToString = toArray.joined(separator: "+")

Or if you're looking for a more Swifty solution that doesn't utilize API from NSString, you could use this.

let aString = "Some search text"

let replaced = String(aString.map {
    $0 == " " ? "+" : $0
})

Swift 3, Swift 4, Swift 5 Solution

let exampleString = "Example string"

//Solution suggested above in Swift 3.0
let stringToArray = exampleString.components(separatedBy: " ")
let stringFromArray = stringToArray.joined(separator: "+")

//Swiftiest solution
let swiftyString = exampleString.replacingOccurrences(of: " ", with: "+")