To get an equirectangular to display interactively you have to deliver it in some interactive viewer format. The most common formats for 360x180 panos would be HTML5, Flash, or QuicktimeVR. The PTGui stitcher, for example, can actually output to QuicktimeVR directly as well as to equirectangulars.
There are a plethora of tools that can do this, and even Facebook and Flickr can do it automatically with uploads that use the appropriate metadata and tagging, respectively. Most will use HTML5 and a web browser.
But if you don't want to use an online service, one tool that will convert any equirectangular image to HTML5, Flash, or QuicktimeVR is Garden Gnome's Pano2VR, but it's licensed. You may also want to look at KrPano.
If you just want to quickly check that a pano you stitched in Hugin looks good, Hugin has a built-in panorama viewer, and a simply using the menu command View → Overview will take you to the Overview pane where you can drag the axes about to rotate the view, but you'll be looking at the sphere from the outside, not the inside. :)