It's certainly possible to develop on a Windows machine, in fact, my first application was exclusively developed on the old Dell Precision I had at the time :)

There are three routes;

1. Install OSx86 (aka iATKOS / Kalyway) on a second partition/disk and dual boot.
2. Run Mac OS X Server under VMWare (Mac OS X 10.7 (Lion) onwards, read the update below).
3. Use Delphi XE4 and the macincloud service. This is a commercial toolset, but the component and lib support is growing.

The first route requires modifying (or using a pre-modified) image of Leopard that can be installed on a regular PC. This is not as hard as you would think, although your success/effort ratio will depend upon how closely the hardware in your PC matches that in Mac hardware - e.g. if you're running a Core 2 Duo on an Intel Motherboard, with an NVidia graphics card you are laughing. If you're running an AMD machine or something without SSE3 it gets a little more involved.

If you purchase (or already own) a version of Leopard then this is a gray area since the Leopard EULA states you may only run it on an "Apple Labeled" machine. As many point out if you stick an Apple sticker on your PC you're probably covered.

The second option is more costly. The EULA for the workstation version of Leopard prevents it from being run under emulation and as a result, there's no support in VMWare for this. Leopard server, however, CAN be run under emulation and can be used for desktop purposes. Leopard server and VMWare are expensive, however.

If you're interested in option 1) I would suggest starting at Insanelymac and reading the OSx86 sections.

I do think you should consider whether the time you will invest is going to be worth the money you will save though. It was for me because I enjoy tinkering with this type of stuff and I started during the early iPhone betas, months before their App Store became available.

Alternatively, you could pick up a low-spec Mac Mini from eBay. You don't need much horsepower to run the SDK and you can always sell it on later if you decide to stop development or buy a better Mac.

Update: You cannot create a Mac OS X Client virtual machine for OS X 10.6 and earlier. Apple does not allow these Client OSes to be virtualized. With Mac OS X 10.7 (Lion) onwards, Apple has changed its licensing agreement in regards to virtualization. Source: VMWare KnowledgeBase

Important: This check should always be performed asynchronously. The majority of answers below are synchronous so be careful otherwise you'll freeze up your app.

Swift

1. Install via CocoaPods or Carthage: https://github.com/ashleymills/Reachability.swift

2. Test reachability via closures

   let reachability = Reachability()!
   
   reachability.whenReachable = { reachability in
       if reachability.connection == .wifi {
           print("Reachable via WiFi")
       } else {
           print("Reachable via Cellular")
       }
   }
   
   reachability.whenUnreachable = { _ in
       print("Not reachable")
   }
   
   do {
       try reachability.startNotifier()
   } catch {
       print("Unable to start notifier")
   }
   

Objective-C

1. Add SystemConfiguration framework to the project but don't worry about including it anywhere

2. Add Tony Million's version of Reachability.h and Reachability.m to the project (found here: https://github.com/tonymillion/Reachability)

3. Update the interface section

   #import "Reachability.h"
   
   // Add this to the interface in the .m file of your view controller
   @interface MyViewController ()
   {
       Reachability *internetReachableFoo;
   }
   @end
   

4. Then implement this method in the .m file of your view controller which you can call

   // Checks if we have an internet connection or not
   - (void)testInternetConnection
   {
       internetReachableFoo = [Reachability reachabilityWithHostname:@"www.google.com"];
   
       // Internet is reachable
       internetReachableFoo.reachableBlock = ^(Reachability*reach)
       {
           // Update the UI on the main thread
           dispatch_async(dispatch_get_main_queue(), ^{
               NSLog(@"Yayyy, we have the interwebs!");
           });
       };
   
       // Internet is not reachable
       internetReachableFoo.unreachableBlock = ^(Reachability*reach)
       {
           // Update the UI on the main thread
           dispatch_async(dispatch_get_main_queue(), ^{
               NSLog(@"Someone broke the internet :(");
           });
       };
   
       [internetReachableFoo startNotifier];
   }
   

Important Note: The Reachability class is one of the most used classes in projects so you might run into naming conflicts with other projects. If this happens, you'll have to rename one of the pairs of Reachability.h and Reachability.m files to something else to resolve the issue.

Note: The domain you use doesn't matter. It's just testing for a gateway to any domain.