Smart App Banners are a recent addition for iOS devices in iOS 6. It involves the simple addition of a meta tag that when visited with Mobile Safari checks for the existence of an App on the phone and shows options for whether the visitor wants to launch or install the App.
<meta name="apple-itunes-app"
content="app-id=myAppId, affiliate-data=myAffiliateData,
app-argument=myArgs" />
Windows Store app linking works similarly:
<meta name="msApplication-ID" content="myAppId" />
<meta name="msApplication-PackageFamilyName"
content="myMicrosoftAppBuildPackageName" />
<meta name="msApplication-Arguments" content="myArgs" />
Are there any similar conventions for Android Apps / Google Play? With mechanisms to pass arguments?
There really isn't. You could register your app to handle certain urls, such as http://app.mydomain.tld although that is somewhat frowned upon by the the more seasoned android folks. If invoked, this url would invoke the app with full URI (which is the mechanism to pass data to it). If the app wasn't installed or set to handle those urls, the browser would then redirect to a page on your server which could prompt for install.