Now Push Notify - iOS does not support browser notifications today, but Now Push Notify makes this possible.
Pusher Beams - Send push notifications programmatically at scale
Mentioned By - Learn when your site is mentioned by other sites for free
PushNinja - by 500apps
Analyzify - Google tag manager and analytics app for your Shopify store
OneSignal Push Notifications for Shopify - Abandoned cart, automated campaigns, robust analytics.