The Webview may not have built-in detectors to auto-link plain URLs within a page, but you could run a JavaScript function within the WebView to parse the URLs when the page finishes loading.
Basically, something like the following (I haven't checked this code for syntax yet, but it should give you the idea):
final WebView webview = (WebView)findViewById(R.id.browser);
/* JavaScript must be enabled if you want it to work, obviously */
webview.getSettings().setJavaScriptEnabled(true);
/* WebViewClient must be set BEFORE calling loadUrl! */
webview.setWebViewClient(new WebViewClient() {
@Override
public void onPageFinished(WebView view, String url)
{
webview.loadUrl("javascript:(function() { " +
"var exp = /(\b(https?|ftp|file):\/\/[-A-Z0-9+&@#\/%?=~_|!:,.;]*[-A-Z0-9+&@#\/%=~_|])/ig; " +
"document.getElementsByTagName('body')[0].innerHTML = document.getElementsByTagName('body')[0].innerHTML.replace(exp,'<a href='$1'>$1</a>');" +
"})()");
}
});
webview.loadUrl("http://code.google.com/android");
Note that the above JavaScript borrows the URL-parsing JavaScript regex from " How to replace plain URLs with links?," and more info can be found on JavaScript injection within the Android WebViewClient reference and at http://lexandera.com/2009/01/injecting-javascript-into-a-webview/ (not me).