iOS: Even if you don't pay attention to your Klout or other scores, you might be curious about the reach of your tweets. Twitter Analytics are typically for business clients, but now anyone with the iOS Twitter app can see these stats.
These stats only work on the iOS version of the official Twitter app (for now). When in the app, just tap on one of your tweets. Underneath will be View Tweet Activity. From there you'll see all the stats on impressions, engagements, favourites and click throughs.