What equipment is needed to take panoramic street photography like in this example.
360x180 panos can be taken with a variety of gear, but they do get harder to take in certain situations.
The first factor, obviously, is scene coverage. Either taking multiple shots or using multiple cameras simultaneously (as Google does), you have to cover the entire sphere. You can use specialized lenses to maximize the coverage per shot, or take more shots and stitch. With a typical rectilinear wide-angle gear (say, an EF-S 10-22 @10mm on a Canon crop body), this may encompass 14 to 24 shots, and requires shooting multiple rows and possibly a zenith (straight up) and nadir (straight down). Or, you could use a fisheye lens and as few as four shots.
The second factor is parallax error. The closer objects of interest are in a panorama like this, the more critical parallax error between member images becomes, and the more you have to rotate the lens around its no-parallax point for a clean stitch. Some scenes allow for handholding, others may require a tripod and specialized panorama head.
A third factor is movement. Multiple images stitched together always holds the potential for creating "ghosts" or "clones" when the images are combined. If you need to capture a spherical view with a lot of moving subjects or from a moving vantage point, then you will need to take all the member images simultaneously, which will require a special multi-camera rig, or you have to be ok with motion blur, or taking multiple shots through time, and masking out the bits of moving things that could cause ghosts/clones.
A fourth factor is your stitching software: not all applications can create a 360x180 panorama, because the internal model of the panorama may be assuming cylindrical presentation or a less-than-360 degree field of view on the stitched panorama. One open source cross-platform package that can do 360x180 panoramas is Hugin.
A fifth factor is presentation of the panorama. Typically, some sort of specialized viewer that can pan through the image on the fly is required, and you need to get the panorama into the proper format for that viewer. There are a number of solutions, mostly based on HTML5 or Flash, but there is no specific universal format (especially since Apple stopped supporting QTVR cubics).
The Google Streetview images are taken with multiple cameras, simultaneously, and then stitched together as a panoramic. They talk all about it here, Street View.
If you wanted to get a similar picture from a stationary location, it can be done with a single digital camera (point and shoot or DSLR) taking multiple pictures. When taking panoramic photos, make sure that each photo overlaps the neighboring photos by at least 40% to allow for enough alignment points. If there are moving people in your photos, it can be tricky to get the pictures to line up properly when using a single camera since a person may show up in multiple pictures.
There are now a number of cameras that will take and automatically stitch spherical photos or video instantly using a small number of fixed very wide angle lenses. Ricoh's Theta line has several cameras that can do this for $350 or less.
Depends on what level of quality you're going for. I'd say the minimum would be using a smartphone and Google's Photo Sphere app.
You could step it up a notch by buying a used Gigapan Epic and a point and shoot camera.
You could try Optonaut as an alternative to Googles Photo Sphere app. The special thing about this app is that you can view the images in 3D via a technique called "stereoscopy". All you need is an Android / iOS smartphone to create the image and a standard smartphone + Cardboard (see Kickstarter below) to see it in 3D. If you want to watch the "normal" photo sphere you can do so via browser.
They currently have a Kickstarter project.
Disclaimer: The developers of that project are friends of mine.