Product Customizer - Creating extremely customizable products within Shopify is no longer a hassle!
BlogFeeder - Automatically pull updates from any RSS feed into your Shopify blog
Happy Ending - Personalize your thank you page
Best (asynchronous): Use the app/uninstalled webhook.
Instant (synchronous): Check if the OAuth token you have is still valid.
Check out my apps: Social Call-to-Action [https://apps.shopify.com/social-call-to-action] and Fliptabify [https://apps.shopify.com/fliptabify]. I also maintain the Shopify API client in PHP [https://github.com/phpish/shopify] and PHP Quickstart Skeletons for building Shopify apps: [https://github.com/phpish/shopify_app-skeleton] and [https://github.com/phpish/shopify_private_app-skeleton]