Tumblr for iOS: Uses a JSON API and Mustache templates like a mobile site would, but does template evaluation on the native side, with the UIWebView just being used to render the resulting HTML. This makes the absence of a JIT less critical.
LinkedIn: Works around the lack of a good web/native bridge by embedding an extremely lightweight HTTP server in the application itself. The HTTP server exposes native functionality through a very simple REST API that can be consumed in the embedded HTML controls through standard JavaScript HTTP requests.
See also this SXSW panel.
Update on 12/7/2012: Tumblr appears to have changed to being purely native.