For a basic viewer, I've been playing with WxGIS Catalog, which does the basics nicely but could use some fleshing out for more complex use cases. There's also RasterCatalog for QGIS, but as the name states, its only for rasters. On OS X, try GISlook, but none of these look to handle the spatial database engines directly.
This question has been converted to Community Wiki and wiki locked
because it is an example of a question that seeks a list of answers
and appears to be popular enough to protect it from closure. It
should be treated as a special case and should not be viewed as the
type of question that is encouraged on this, or any Stack Exchange
site, but if you wish to contribute more content to it then feel free
to do so by editing this answer.
There are quite a few alternatives and I've actually written a short book on the subject entitled "Online GIS - Meet the Cloud Publication Platforms that Will Revolutionize our Industry" but that's a little outdated now.
Here's an updated summary:
MangoMap: Very easy to use, no coding required. Lots of tools and functionality available to make really polished map applications. Much more competitive pricing than ArcGIS Online organisational accounts.
GISCloud: Online alternative to traditional client/server GIS setup. Many features but hampered by a frustrating user interface.
MapBox: Making maps sexy again. Programmer focused. Great for maps that need to fit a brand and be able to scale for high traffic. Good fit for consumer internet sites.
CartoDB: Attractive UX and scales very well. Also lets you preserve the Google Maps experience for end users. Postgres + postgis database on the cloud with a set of API's on top of it to fetch/save and render data.
Disclosure: Original answer posted by Founder of MangoMaps and includes an edit by the CTO of CartoDB - these two products are described in this answer.
I've had good luck using GeoCommons for more lightweight mapping.
The upside is that the service is free within a certain limit, and includes some fairly powerful analysis tools. I believe any mapping is free if using or creating open data, and while my organization did not end up paying for the service, the prices seemed reasonable.
I didn't realize until I visited today, though, that this service is now a part of esri, so their terms may have changed.
Best Answer
The closest thing to what you want that I could think of is GeoNode.
It allows you to upload files, create and edit maps and metadata, and also to rate the data. You can also embed the maps you create in GeoNode on your own web pages. The data is downloadable as well. The following are the supported export formats:
The latest release has support for comments and ratings on map and layers. It also has social features( e.g. you can ‘like’ a layer on Facebook and ‘+1′ it on Google Plus ).