After reading through the other answers on here (and needing to support other hash types as well) I wrote a String extension that handles multiple hash types and output types.
NOTE: CommonCrypto is included in Xcode 10, so you can simply import CommonCrypto without having to mess with a bridging header if you have the latest Xcode version installed... Otherwise a bridging header is necessary.
UPDATE: Both Swift 4 & 5 use the same String+Crypto.swift file below. 
There is a separate Data+Crypto.swift file for Swift 5 (see below) as the api for 'withUnsafeMutableBytes' and 'withUnsafeBytes' changed between Swift 4 & 5.
String+Crypto.swift -- (for both Swift 4 & 5)
import Foundation
import CommonCrypto
// Defines types of hash string outputs available
public enum HashOutputType {
    // standard hex string output
    case hex
    // base 64 encoded string output
    case base64
}
// Defines types of hash algorithms available
public enum HashType {
    case md5
    case sha1
    case sha224
    case sha256
    case sha384
    case sha512
    var length: Int32 {
        switch self {
        case .md5: return CC_MD5_DIGEST_LENGTH
        case .sha1: return CC_SHA1_DIGEST_LENGTH
        case .sha224: return CC_SHA224_DIGEST_LENGTH
        case .sha256: return CC_SHA256_DIGEST_LENGTH
        case .sha384: return CC_SHA384_DIGEST_LENGTH
        case .sha512: return CC_SHA512_DIGEST_LENGTH
        }
    }
}
public extension String {
    /// Hashing algorithm for hashing a string instance.
    ///
    /// - Parameters:
    ///   - type: The type of hash to use.
    ///   - output: The type of output desired, defaults to .hex.
    /// - Returns: The requested hash output or nil if failure.
    public func hashed(_ type: HashType, output: HashOutputType = .hex) -> String? {
        // convert string to utf8 encoded data
        guard let message = data(using: .utf8) else { return nil }
        return message.hashed(type, output: output)
    } 
}
SWIFT 5 -- Data+Crypto.swift
import Foundation
import CommonCrypto
extension Data {
    /// Hashing algorithm that prepends an RSA2048ASN1Header to the beginning of the data being hashed.
    ///
    /// - Parameters:
    ///   - type: The type of hash algorithm to use for the hashing operation.
    ///   - output: The type of output string desired.
    /// - Returns: A hash string using the specified hashing algorithm, or nil.
    public func hashWithRSA2048Asn1Header(_ type: HashType, output: HashOutputType = .hex) -> String? {
        let rsa2048Asn1Header:[UInt8] = [
            0x30, 0x82, 0x01, 0x22, 0x30, 0x0d, 0x06, 0x09, 0x2a, 0x86, 0x48, 0x86,
            0xf7, 0x0d, 0x01, 0x01, 0x01, 0x05, 0x00, 0x03, 0x82, 0x01, 0x0f, 0x00
        ]
        var headerData = Data(rsa2048Asn1Header)
        headerData.append(self)
        return hashed(type, output: output)
    }
    /// Hashing algorithm for hashing a Data instance.
    ///
    /// - Parameters:
    ///   - type: The type of hash to use.
    ///   - output: The type of hash output desired, defaults to .hex.
    ///   - Returns: The requested hash output or nil if failure.
    public func hashed(_ type: HashType, output: HashOutputType = .hex) -> String? {
        // setup data variable to hold hashed value
        var digest = Data(count: Int(type.length))
        _ = digest.withUnsafeMutableBytes{ digestBytes -> UInt8 in
            self.withUnsafeBytes { messageBytes -> UInt8 in
                if let mb = messageBytes.baseAddress, let db = digestBytes.bindMemory(to: UInt8.self).baseAddress {
                    let length = CC_LONG(self.count)
                    switch type {
                    case .md5: CC_MD5(mb, length, db)
                    case .sha1: CC_SHA1(mb, length, db)
                    case .sha224: CC_SHA224(mb, length, db)
                    case .sha256: CC_SHA256(mb, length, db)
                    case .sha384: CC_SHA384(mb, length, db)
                    case .sha512: CC_SHA512(mb, length, db)
                    }
                }
                return 0
            }
        }
        // return the value based on the specified output type.
        switch output {
        case .hex: return digest.map { String(format: "%02hhx", $0) }.joined()
        case .base64: return digest.base64EncodedString()
        }
    }
}
SWIFT 4 -- Data+Crypto.swift
import Foundation
import CommonCrypto 
extension Data {
    /// Hashing algorithm that prepends an RSA2048ASN1Header to the beginning of the data being hashed.
    ///
    /// - Parameters:
    ///   - type: The type of hash algorithm to use for the hashing operation.
    ///   - output: The type of output string desired.
    /// - Returns: A hash string using the specified hashing algorithm, or nil.
    public func hashWithRSA2048Asn1Header(_ type: HashType, output: HashOutputType = .hex) -> String? {
        let rsa2048Asn1Header:[UInt8] = [
            0x30, 0x82, 0x01, 0x22, 0x30, 0x0d, 0x06, 0x09, 0x2a, 0x86, 0x48, 0x86,
            0xf7, 0x0d, 0x01, 0x01, 0x01, 0x05, 0x00, 0x03, 0x82, 0x01, 0x0f, 0x00
        ]
        var headerData = Data(bytes: rsa2048Asn1Header)
        headerData.append(self)
        return hashed(type, output: output)
    }
    /// Hashing algorithm for hashing a Data instance.
    ///
    /// - Parameters:
    ///   - type: The type of hash to use.
    ///   - output: The type of hash output desired, defaults to .hex.
    ///   - Returns: The requested hash output or nil if failure.
    public func hashed(_ type: HashType, output: HashOutputType = .hex) -> String? {
        // setup data variable to hold hashed value
        var digest = Data(count: Int(type.length))
        // generate hash using specified hash type
        _ = digest.withUnsafeMutableBytes { (digestBytes: UnsafeMutablePointer<UInt8>) in
            self.withUnsafeBytes { (messageBytes: UnsafePointer<UInt8>) in
                let length = CC_LONG(self.count)
                switch type {
                case .md5: CC_MD5(messageBytes, length, digestBytes)
                case .sha1: CC_SHA1(messageBytes, length, digestBytes)
                case .sha224: CC_SHA224(messageBytes, length, digestBytes)
                case .sha256: CC_SHA256(messageBytes, length, digestBytes)
                case .sha384: CC_SHA384(messageBytes, length, digestBytes)
                case .sha512: CC_SHA512(messageBytes, length, digestBytes)
                }
            }
        }
        // return the value based on the specified output type.
        switch output {
        case .hex: return digest.map { String(format: "%02hhx", $0) }.joined()
        case .base64: return digest.base64EncodedString()
        }
    }
}
Edit: since the hash actually happens on the Data, I split the hashing algorithm out into a Data extension. This allows the same algorithm to be used for SSL Certificate pinning hash operations as well.
Here's a short example of how you might use it for an SSL Pinning operation:
// Certificate pinning - get certificate as data
let data: Data = SecCertificateCopyData(serverCertificate) as Data
// compare hash of server certificate with local (expected) hash value
guard let serverHash = data.hashWithRSA2048Asn1Header(.sha256, output: .base64), serverHash == storedHash else {
    print("SSL PINNING: Server certificate hash does not match specified hash value.")
    return false
}
back to the original answer
I tested the hash algorithms using this:
let value = "This is my string"
if let md5 = value.hashed(.md5) {
    print("md5: \(md5)")
}
if let sha1 = value.hashed(.sha1) {
    print("sha1: \(sha1)")
}
if let sha224 = value.hashed(.sha224) {
    print("sha224: \(sha224)")
}
if let sha256 = value.hashed(.sha256) {
    print("sha256: \(sha256)")
}
if let sha384 = value.hashed(.sha384) {
    print("sha384: \(sha384)")
}
if let sha512 = value.hashed(.sha512) {
    print("sha512: \(sha512)")
}
and this is the printed results:
md5: c2a9ce57e8df081b4baad80d81868bbb
sha1: 37fb219bf98bee51d2fdc3ba6d866c97f06c8223
sha224: f88e2f20aa89fb4dffb6bdc62d7bd75e1ba02574fae4a437c3bf49c7
sha256: 9da6c02379110815278b615f015f0b254fd3d5a691c9d8abf8141655982c046b
sha384: d9d7fc8aefe7f8f0a969b132a59070836397147338e454acc6e65ca616099d03a61fcf9cc8c4d45a2623145ebd398450
sha512: 349cc35836ba85915ace9d7f895b712fe018452bb4b20ff257257e12adeb1e83ad780c6568a12d03f5b2cb1e3da23b8b7ced9012a188ef3855e0a8f3db211883