A web-based beta version of Nintendo’s Miiverse social network is now accessible via the PC and mobile devices. You can access the network at this link: https://miiverse.nintendo.net/
Since this web version of Miiverse is currently in beta, not all features are available yet, including the ability to make new posts in a community, send and receive messages, send/receive friend requests, and follow/unfollow users. In short, at the moment you’re limited to browsing the Miiverse, unless you access it via a Wii U. In fact, can only create a Miiverse account from a Wii U at the moment.
Nintendo will also be bringing the Miiverse to the Nintendo 3DS at some point.