Solution for Swift 3.1 for orientation issue while capturing the image from Camera.
I have updated the solution given by jake and Metal Heart
UIImage extension
//MARK:- Image Orientation fix
extension UIImage {
    func fixOrientation() -> UIImage {
        // No-op if the orientation is already correct
        if ( self.imageOrientation == UIImageOrientation.up ) {
            return self;
        }
        // We need to calculate the proper transformation to make the image upright.
        // We do it in 2 steps: Rotate if Left/Right/Down, and then flip if Mirrored.
        var transform: CGAffineTransform = CGAffineTransform.identity
        if ( self.imageOrientation == UIImageOrientation.down || self.imageOrientation == UIImageOrientation.downMirrored ) {
            transform = transform.translatedBy(x: self.size.width, y: self.size.height)
            transform = transform.rotated(by: CGFloat(Double.pi))
        }
        if ( self.imageOrientation == UIImageOrientation.left || self.imageOrientation == UIImageOrientation.leftMirrored ) {
            transform = transform.translatedBy(x: self.size.width, y: 0)
            transform = transform.rotated(by: CGFloat(Double.pi / 2.0))
        }
        if ( self.imageOrientation == UIImageOrientation.right || self.imageOrientation == UIImageOrientation.rightMirrored ) {
            transform = transform.translatedBy(x: 0, y: self.size.height);
            transform = transform.rotated(by: CGFloat(-Double.pi / 2.0));
        }
        if ( self.imageOrientation == UIImageOrientation.upMirrored || self.imageOrientation == UIImageOrientation.downMirrored ) {
            transform = transform.translatedBy(x: self.size.width, y: 0)
            transform = transform.scaledBy(x: -1, y: 1)
        }
        if ( self.imageOrientation == UIImageOrientation.leftMirrored || self.imageOrientation == UIImageOrientation.rightMirrored ) {
            transform = transform.translatedBy(x: self.size.height, y: 0);
            transform = transform.scaledBy(x: -1, y: 1);
        }
        // Now we draw the underlying CGImage into a new context, applying the transform
        // calculated above.
        let ctx: CGContext = CGContext(data: nil, width: Int(self.size.width), height: Int(self.size.height),
                                                      bitsPerComponent: self.cgImage!.bitsPerComponent, bytesPerRow: 0,
                                                      space: self.cgImage!.colorSpace!,
                                                      bitmapInfo: self.cgImage!.bitmapInfo.rawValue)!;
        ctx.concatenate(transform)
        if ( self.imageOrientation == UIImageOrientation.left ||
            self.imageOrientation == UIImageOrientation.leftMirrored ||
            self.imageOrientation == UIImageOrientation.right ||
            self.imageOrientation == UIImageOrientation.rightMirrored ) {
            ctx.draw(self.cgImage!, in: CGRect(x: 0,y: 0,width: self.size.height,height: self.size.width))
        } else {
            ctx.draw(self.cgImage!, in: CGRect(x: 0,y: 0,width: self.size.width,height: self.size.height))
        }
        // And now we just create a new UIImage from the drawing context and return it
        return UIImage(cgImage: ctx.makeImage()!)
    }
}
Swift 2.0
//MARK:- Image Orientation fix
extension UIImage {
    func fixOrientation() -> UIImage {
        // No-op if the orientation is already correct
        if ( self.imageOrientation == UIImageOrientation.Up ) {
            return self;
        }
        // We need to calculate the proper transformation to make the image upright.
        // We do it in 2 steps: Rotate if Left/Right/Down, and then flip if Mirrored.
        var transform: CGAffineTransform = CGAffineTransformIdentity
        if ( self.imageOrientation == UIImageOrientation.Down || self.imageOrientation == UIImageOrientation.DownMirrored ) {
            transform = CGAffineTransformTranslate(transform, self.size.width, self.size.height)
            transform = CGAffineTransformRotate(transform, CGFloat(M_PI))
        }
        if ( self.imageOrientation == UIImageOrientation.Left || self.imageOrientation == UIImageOrientation.LeftMirrored ) {
            transform = CGAffineTransformTranslate(transform, self.size.width, 0)
            transform = CGAffineTransformRotate(transform, CGFloat(M_PI_2))
        }
        if ( self.imageOrientation == UIImageOrientation.Right || self.imageOrientation == UIImageOrientation.RightMirrored ) {
            transform = CGAffineTransformTranslate(transform, 0, self.size.height);
            transform = CGAffineTransformRotate(transform,  CGFloat(-M_PI_2));
        }
        if ( self.imageOrientation == UIImageOrientation.UpMirrored || self.imageOrientation == UIImageOrientation.DownMirrored ) {
            transform = CGAffineTransformTranslate(transform, self.size.width, 0)
            transform = CGAffineTransformScale(transform, -1, 1)
        }
        if ( self.imageOrientation == UIImageOrientation.LeftMirrored || self.imageOrientation == UIImageOrientation.RightMirrored ) {
            transform = CGAffineTransformTranslate(transform, self.size.height, 0);
            transform = CGAffineTransformScale(transform, -1, 1);
        }
        // Now we draw the underlying CGImage into a new context, applying the transform
        // calculated above.
        let ctx: CGContextRef = CGBitmapContextCreate(nil, Int(self.size.width), Int(self.size.height),
            CGImageGetBitsPerComponent(self.CGImage), 0,
            CGImageGetColorSpace(self.CGImage),
            CGImageGetBitmapInfo(self.CGImage).rawValue)!;
        CGContextConcatCTM(ctx, transform)
        if ( self.imageOrientation == UIImageOrientation.Left ||
            self.imageOrientation == UIImageOrientation.LeftMirrored ||
            self.imageOrientation == UIImageOrientation.Right ||
            self.imageOrientation == UIImageOrientation.RightMirrored ) {
                CGContextDrawImage(ctx, CGRectMake(0,0,self.size.height,self.size.width), self.CGImage)
        } else {
            CGContextDrawImage(ctx, CGRectMake(0,0,self.size.width,self.size.height), self.CGImage)
        }
        // And now we just create a new UIImage from the drawing context and return it
        return UIImage(CGImage: CGBitmapContextCreateImage(ctx)!)
    }
}
Use of this UIImage Extension in your code:
let fixOrientationImage=chosenImage.fixOrientation()
place this in your delegate methods of image picker like this
Swift 3.1
//MARK: Image Picker Delegates
    func imagePickerController(
        _ picker: UIImagePickerController,
        didFinishPickingMediaWithInfo info: [String : Any]){
        let chosenImage = info[UIImagePickerControllerOriginalImage] as! UIImage
        profileImg.contentMode = .scaleAspectFill
        let fixOrientationImage=chosenImage.fixOrientation()
        profileImg.image = fixOrientationImage
        dismiss(animated: true, completion: nil)
    }
Swift 2.0
//MARK: Image Picker Delegates
    func imagePickerController(
        picker: UIImagePickerController,
        didFinishPickingMediaWithInfo info: [String : AnyObject])
    {
        let chosenImage = info[UIImagePickerControllerOriginalImage] as! UIImage
        profileImg.contentMode = .ScaleAspectFill
        **//Fix the image orientation**
         let fixOrientationImage=chosenImage.fixOrientation()
        profileImg.image = fixOrientationImage
        dismissViewControllerAnimated(true, completion: nil)
    }