I haven't posted about specific web apps or services here much yet, but Forecast is worth drawing to your attention. I always wanted to try out the Dark Sky iOS weather app, but it was US-only. Now the Dark Sky team has developed a complete global weather application as a web-app. It works beautifully in Safari on Mac and on iPhone/iPad, with delightfully smooth animations (and a great Time Machine feature on desktop browsers that lets you check weather on a given historical date). I could stare at Forecast's updating near-term weather predictions for hours.
I'm generally a bit sniffy about web apps–I'd much sooner have a native app–but if this is the standard we can expect then I'm just fine with that.