You can add your table view to a container view and add drop shadow to that container view:
let containerView:UIView = UIView(frame:CGRect(x: 10, y: 100, width: 300, height: 400))
self.tableView = UITableView(frame: containerView.bounds), style: .Plain)
containerView.backgroundColor = UIColor.clearColor()
containerView.layer.shadowColor = UIColor.darkGrayColor().CGColor
containerView.layer.shadowOffset = CGSize(width: 2.0, height: 2.0)
containerView.layer.shadowOpacity = 1.0
containerView.layer.shadowRadius = 2
// This is for rounded corners
self.tableView.layer.cornerRadius = 10
self.tableView.layer.masksToBounds = true
self.view.addSubview(containerView)
containerView.addSubview(self.tableView)
Edit
Swift 3.0:
let containerView:UIView = UIView(frame:CGRect(x: 10, y: 100, width: 300, height: 400))
self.tableView = UITableView(frame: containerView.bounds, style: .plain)
containerView.backgroundColor = UIColor.clear
containerView.layer.shadowColor = UIColor.darkGray.cgColor
containerView.layer.shadowOffset = CGSize(width: 2.0, height: 2.0)
containerView.layer.shadowOpacity = 1.0
containerView.layer.shadowRadius = 2
self.tableView.layer.cornerRadius = 10
self.tableView.layer.masksToBounds = true
self.view.addSubview(containerView)
containerView.addSubview(self.tableView)
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