MoboMarket is an interesting third-party Android app marketplace with plenty of apps you won't find on Google Play. It does require you to double-check before downloading, as there are lots of duplicates of Google's Play Store offerings and several questionable apps that seem to do more harm than good. Still, if you dislike Google Play, this is a good app to have handy.
In addition to letting you choose new apps, you can download extra themes and wallpapers from this marketplace. It isn't hosted by Google Play, so you'll need a third-party installer to make it work. It seems like this marketplace exists to host apps that wouldn't be approved by Google, so there are some adult apps to be found here, too. There are plenty of familiar faces that top the Google Play charts, as well, but some of them aren't real apps. Make sure you double-check permissions and fine print before you install anything from MoboMarket. To try to make things easier, the app offers verified reviews that can help weed out scams. In addition, we have to give this marketplace a thumbs up for sporting a very comfortable layout, which makes downloading apps remarkably easy.
Though MoboMarket might turn some people off, many people are desperate for an app marketplace that isn't related to Google. No matter what your reasons for shying away from the Play store, MoboMarket fills the hole quite well. It's a great way to download some of the most popular apps as well as a few you won't find on Google Play.