iOS Equivalent For Android Shared Preferences

Use NSUserDefaults: - note that this is for small bits of data, such as the current level like you mentioned. Don't abuse this and use it as a large database, because it is loaded into memory every time you open your app, whether you need something from it or not (other parts of your app will also use this).

Objective-C:

Reading:

NSUserDefaults *preferences = [NSUserDefaults standardUserDefaults];

NSString *currentLevelKey = @"currentlevel";

if ([preferences objectForKey:currentLevelKey] == nil)
{
    //  Doesn't exist.
}
else
{
    //  Get current level
    const NSInteger currentLevel = [preferences integerForKey:currentLevelKey];
}

Writing:

NSUserDefaults *preferences = [NSUserDefaults standardUserDefaults];

NSString *currentLevelKey = @"currentlevel";

const NSInteger currentLevel = ...;
[preferences setInteger:currentLevel forKey:currentLevelKey];

//  Save to disk
const BOOL didSave = [preferences synchronize];

if (!didSave)
{
    //  Couldn't save (I've never seen this happen in real world testing)
}

.

Swift:

Reading:

let preferences = NSUserDefaults.standardUserDefaults()

let currentLevelKey = "currentLevel"

if preferences.objectForKey(currentLevelKey) == nil {
    //  Doesn't exist
} else {
    let currentLevel = preferences.integerForKey(currentLevelKey)
}

Writing:

let preferences = NSUserDefaults.standardUserDefaults()

let currentLevelKey = "currentLevel"

let currentLevel = ...
preferences.setInteger(currentLevel, forKey: currentLevelKey)

//  Save to disk
let didSave = preferences.synchronize()

if !didSave {
    //  Couldn't save (I've never seen this happen in real world testing)
}

Here is an update for Swift 3

Reading

let preferences = UserDefaults.standard

let currentLevelKey = "currentLevel"
if preferences.object(forKey: currentLevelKey) == nil {
    //  Doesn't exist
} else {
    let currentLevel = preferences.integer(forKey: currentLevelKey)
}

Writing

let preferences = UserDefaults.standard

let currentLevel = ...
let currentLevelKey = "currentLevel"
preferences.set(currentLevel, forKey: currentLevelKey)

Update

From UserDefaults documentation

synchronize() waits for any pending asynchronous updates to the defaults database and returns; this method is now unnecessary and shouldn't be used.