In Swift, is it possible to convert a string to an enum?

Sure. Enums can have a raw value. To quote the docs:

Raw values can be strings, characters, or any of the integer or floating-point number types

— Excerpt From: Apple Inc. “The Swift Programming Language.” iBooks. https://itun.es/us/jEUH0.l,

So you can use code like this:

enum StringEnum: String 
{
    case one   = "value one"
    case two   = "value two"
    case three = "value three"
}

let anEnum = StringEnum(rawValue: "value one")!

print("anEnum = \"\(anEnum.rawValue)\"")

Note: You don't need to write = "one" etc. after each case. The default string values are the same as the case names so calling .rawValue will just return a string

EDIT

If you need the string value to contain things like spaces that are not valid as part of a case value then you need to explicitly set the string. So,

enum StringEnum: String 
{
  case one
  case two
  case three
}

let anEnum = StringEnum.one
print("anEnum = \"\(anEnum)\"")

gives

anEnum = "one"

But if you want case one to display "value one" you will need to provide the string values:

enum StringEnum: String 
{
  case one   = "value one"
  case two   = "value two"
  case three = "value three"
}

In Swift 4.2, the CaseIterable protocol can be used for an enum with rawValues, but the string should match against the enum case labels:

enum MyCode : String, CaseIterable {

    case one   = "uno"
    case two   = "dos"
    case three = "tres"

    static func withLabel(_ label: String) -> MyCode? {
        return self.allCases.first{ "\($0)" == label }
    }
}

usage:

print(MyCode.withLabel("one")) // Optional(MyCode.one)
print(MyCode(rawValue: "uno"))  // Optional(MyCode.one)

All you need is:

enum Foo: String {
   case a, b, c, d
}

let a = Foo(rawValue: "a")
assert(a == Foo.a)

let 💩 = Foo(rawValue: "💩")
assert(💩 == nil)

In case with an enum with Int type you can do it so:

enum MenuItem: Int {
    case One = 0, Two, Three, Four, Five //... as much as needs

    static func enumFromString(string:String) -> MenuItem? {
        var i = 0
        while let item = MenuItem(rawValue: i) {
            if String(item) == string { return item }
            i += 1
        }
        return nil
    }
}

And use:

let string = "Two"
if let item = MenuItem.enumFromString(string) {
    //in this case item = 1 
    //your code
} 

Riffing on djruss70's answer to create highly generalized solution:

extension CaseIterable {
    static func from(string: String) -> Self? { Self.allCases.first { string == "\($0)" } }
    func toString() -> String { "\(self)" }
}

Usage:

enum Chassis: CaseIterable {
    case pieridae, oovidae
}

let chassis: Chassis = Chassis.from(string: "oovidae")!
let string: String = chassis.toString()

Note: this will unfortunately not work if the enum is declared @objc. As far as I know as of Swift 5.3 there is no way to get this to work with @objc enum's except brute force solutions (a switch statement).

If someone happens to know of a way to make this work for @objc enums, I'd be very interested in the answer.

Swift 4.2:

public enum PaymentPlatform: String, CaseIterable {
    case visa = "Visa card"
    case masterCard = "Master card"
    case cod = "Cod"

    var nameEnum: String {
        return Mirror(reflecting: self).children.first?.label ?? String(describing: self)
    }

    func byName(name: String) -> PaymentPlatform {
        return PaymentPlatform.allCases.first(where: {$0.nameEnum.elementsEqual(name)}) ?? .cod
    }
}

I found the other answers make this way more complicated then it needs to be. Here is a quick and concise example.

enum Gender: String {
    case male, female, unspecified
}

Simple enum, note that I added ": String" to the enum itself to declare the type as string.

Now all you have to do is:

let example: Gender? = Gender(rawValue: "male")

And thats it, example is now an enum of type Gender with the value of .male

Note that of course nil is returned if there's no such value.

let example: Gender? = Gender(rawValue: "xxx")

example is nil.

There is literally nothing else you need to do in Swift 4+.

Extending Duncan C's answer

extension StringEnum: StringLiteralConvertible {

    init(stringLiteral value: String){
        self.init(rawValue: value)!
    }

    init(extendedGraphemeClusterLiteral value: String) {
        self.init(stringLiteral: value)
    }

    init(unicodeScalarLiteral value: String) {
        self.init(stringLiteral: value)
    }
}

For Int enum and their String representation, I declare enum as follows:

enum OrderState: Int16, CustomStringConvertible {

    case waiting = 1
    case inKitchen = 2
    case ready = 3

    var description: String {
        switch self {
        case .waiting:
            return "Waiting"
        case .inKitchen:
            return "InKitchen"
        case .ready:
            return "Ready"
        }
    }

    static func initialize(stringValue: String)-> OrderState? {
        switch stringValue {
        case OrderState.waiting.description:
            return OrderState.waiting
        case OrderState.inKitchen.description:
            return OrderState.inKitchen
        case OrderState.ready.description:
            return OrderState.ready

        default:
            return nil
        }
    }
}

Usage:

order.orderState = OrderState.waiting.rawValue

let orderState = OrderState.init(rawValue: order.orderState)
let orderStateStr = orderState?.description ?? ""
print("orderStateStr = \(orderStateStr)")

I used this:

public enum Currency: CaseIterable, Codable {
    case AFN = 971 // Afghani (minor=2)
    case DZD = 012 // Algerian Dinar (minor=2)

...

    private static var cachedLookup: [String: Currency] = [:]
    
    init?(string: String) {
        if Self.cachedLookup.isEmpty {
            Self.cachedLookup = Dictionary(uniqueKeysWithValues: Self.allCases.map { ("\($0)", $0) })
        }
        
        if let currency = Self.cachedLookup[string] {
            self = currency
            return
        } else {
            return nil
        }
    }
}