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

For iOS 13:

Use the .shadowColor property

If this property is nil or contains the clear color, the bar displays no shadow

For instance:

let navigationBar = navigationController?.navigationBar
let navigationBarAppearance = UINavigationBarAppearance()
navigationBarAppearance.shadowColor = .clear
navigationBar?.scrollEdgeAppearance = navigationBarAppearance

For iOS 12 and below:

To do this, you should set a custom shadow image. But for the shadow image to be shown you also need to set a custom background image, quote from Apple's documentation:

For a custom shadow image to be shown, a custom background image must also be set with the setBackgroundImage(_:for:) method. If the default background image is used, then the default shadow image will be used regardless of the value of this property.

So:

let navigationBar = navigationController!.navigationBar
navigationBar.setBackgroundImage(#imageLiteral(resourceName: "BarBackground"),
                                                        for: .default)
navigationBar.shadowImage = UIImage()

Above is the only "official" way to hide it. Unfortunately, it removes bar's translucency.

I don't want background image, just color##

You have those options:

1. Solid color, no translucency:

    navigationBar.barTintColor = UIColor.redColor()
    navigationBar.isTranslucent = false
    navigationBar.setBackgroundImage(UIImage(), for: .default)
    navigationBar.shadowImage = UIImage()
   

2. Create small background image filled with color and use it.

3. Use 'hacky' method described below. It will also keep bar translucent.

How to keep bar translucent?##

To keep translucency you need another approach, it looks like a hack but works well. The shadow we're trying to remove is a hairline UIImageView somewhere under UINavigationBar. We can find it and hide/show it when needed.

Instructions below assume you need hairline hidden only in one controller of your UINavigationController hierarchy.

1. Declare instance variable:

   private var shadowImageView: UIImageView?
   

2. Add method which finds this shadow (hairline) UIImageView:

   private func findShadowImage(under view: UIView) -> UIImageView? {
       if view is UIImageView && view.bounds.size.height <= 1 {
           return (view as! UIImageView)
       }
   
       for subview in view.subviews {
           if let imageView = findShadowImage(under: subview) {
               return imageView
           }
       }
       return nil
   }
   

3. Add/edit viewWillAppear/viewWillDisappear methods:

   override func viewWillAppear(_ animated: Bool) {
       super.viewWillAppear(animated)
   
       if shadowImageView == nil {
           shadowImageView = findShadowImage(under: navigationController!.navigationBar)
       }
       shadowImageView?.isHidden = true
   }
   
   override func viewWillDisappear(_ animated: Bool) {
       super.viewWillDisappear(animated)
   
       shadowImageView?.isHidden = false
   }
   

The same method should also work for UISearchBar hairline, and (almost) anything else you need to hide :)

Many thanks to @Leo Natan for the original idea!