Alternatapps - When people moan about no app for X on WP
I have seen many people complain about the lack of X app for Windows Phone over my time on The Verge and now I've finally taken the leap and got myself a WP8 (Nokia Lumia 520), its taken some looking but there are some very good 3rd Party Alternatives provided by the developer community and ones that some people aren't using yet.
Facebook Beta (Microsoft) - I know this doesn't really count but it's a huge improvement over the old app and brings it up to Android and iOS levels of functionality. Still has a few bugs though.
Swapchat - A snapchat client for Windows Phone 8. Looks nicer than the app on Android and iOS but doesn't have push notifications (yet)
MetroTube - A YouTube client for Windows Phone 8, pretty nice looking and works well too. Provides additional functionality that Microsoft's new client won't be able to produce because of Google (downloading et al.) Microsoft's new client will be an option and is looking pretty good anyway
Instance - INSTAGRAM but for Windows Phone, and before you ask. Yes you can post phones with it (probably, there's a camera feature on the screenshots but I don't "get" instagram, it would be pointless otherwise)
Nova 3 - Can't play it myself because I don't have 1GB RAM, but it looks awesome. And you can get it for free if you have a Nokia and change your region to India (where it's a Nokia exclusive)
Survivalcraft - Minecraft for Windows Phone, the controls are still a little awkward but it gets updates more often than the official version and it supports texture packs and more items.
Jetpack Joyride - Works just like the one on iOS and Android
Office - Good, provided by default and opens Word, Excel, PowerPoint docs on the go. The only fault is you can't make your own "New" PowerPoint presentation. I'm not saying office is everything and I don't want a troll argument about it in the comments below, but for free there's no point in ignoring it.
Now the Windows Phone ecosystem is not as full as other app stores, but at least there are all the main apps. If there's something you want especially comment below and I might be able to find it for you on the store.