Change Background of UICollectionView Cell on Tap

Here is my solution. And I'm sure it really works.
I provide three methods to highlight a cell (selectedBackgroundView, tint cell.contentView and tint a special area).

How to use:
1. just inherit BaseCollectionViewCell and do nothing;
2. inherit and set specialHighlightedArea = UIView(), and contentView.addSubView(specialHighlightedArea), then layout it or add constraint to use Auto Layout;
3. if you don't need highlight effect, just write a method named 'shouldHighlightItemAtIndexPath' defined by UICollectionViewDelegate and make it return false, or set cell.shouldTintBackgroundWhenSelected = false and set specialHighlightedArea = nil and remove it from superView.

/// same with UITableViewCell's selected backgroundColor
private let highlightedColor = UIColor(rgb: 0xD8D8D8) 

/// you can make all your collectionViewCell inherit BaseCollectionViewCell
class BaseCollectionViewCell: UICollectionViewCell {

    /// change it as you wish when or after initializing
    var shouldTintBackgroundWhenSelected = true

    /// you can give a special view when selected
    var specialHighlightedArea: UIView? 

    // make lightgray background display immediately(使灰背景立即出现)
    override var isHighlighted: Bool { 
        willSet {
            onSelected(newValue)
        }
    }

    // keep lightGray background until unselected (保留灰背景)
    override var isSelected: Bool { 
        willSet {
            onSelected(newValue)
        }
    }

    func onSelected(_ newValue: Bool) {
        guard selectedBackgroundView == nil else { return }
        if shouldTintBackgroundWhenSelected {
            contentView.backgroundColor = newValue ? highlightedColor : UIColor.clear
        }
        if let area = specialHighlightedArea {
            area.backgroundColor = newValue ? UIColor.black.withAlphaComponent(0.4) : UIColor.clear
        }
    }
}

extension UIColor {
    convenience init(rgb: Int, alpha: CGFloat = 1.0) {
        self.init(red: CGFloat((rgb & 0xFF0000) >> 16) / 255.0, green: CGFloat((rgb & 0xFF00) >> 8) / 255.0, blue: CGFloat(rgb & 0xFF) / 255.0, alpha: alpha)
    }
}

The problem is that you are changing the color on highlight and changing it back on deselect instead that on unhighlight

You should simply change this:

- (void)collectionView:(UICollectionView *)collectionView didDeselectItemAtIndexPath:(NSIndexPath *)indexPath
{
  UICollectionViewCell *cell = [collectionView cellForItemAtIndexPath:indexPath];
  cell.contentView.backgroundColor = [UIColor greenColor];
}

to this:

- (void)collectionView:(UICollectionView *)collectionView didUnhighlightItemAtIndexPath:(NSIndexPath *)indexPath
{
  UICollectionViewCell *cell = [collectionView cellForItemAtIndexPath:indexPath];
  cell.contentView.backgroundColor = [UIColor greenColor];
}

Also, if you don't want to wait a bit before getting your highlight happen you should set the delaysContentTouches property of the collection view to NO

Edit: also ensure that you call

[collectionView deselectItemAtIndexPath:indexPath animated:NO];

inside the -didSelectItemAtIndexPath method

Edit: Answer in Swift 3

var selectedIndex = Int ()

func collectionView(_ collectionView: UICollectionView, cellForItemAt indexPath: IndexPath) -> UICollectionViewCell
{
    let cell = collectionView.dequeueReusableCell(withReuseIdentifier: "cell", for: indexPath) as! CollectionViewCell

    cell.backgroundColor = selectedIndex == indexPath.row ? UIColor.green : UIColor.red

    return cell
}

func collectionView(_ collectionView: UICollectionView, didSelectItemAt indexPath: IndexPath)
{
    selectedIndex = indexPath.row

    self.yourCollctionView.reloadData()
}

Swift 3 version

Add the following two methods to your view controller class:

// change background color when user touches cell
func collectionView(_ collectionView: UICollectionView, didHighlightItemAt indexPath: IndexPath) {
    let cell = collectionView.cellForItem(at: indexPath)
    cell?.backgroundColor = UIColor.red
}

// change background color back when user releases touch
func collectionView(_ collectionView: UICollectionView, didUnhighlightItemAt indexPath: IndexPath) {
    let cell = collectionView.cellForItem(at: indexPath)
    cell?.backgroundColor = UIColor.green
}

See here for help in setting up a basic collection view in Swift.