List of Android Marketplaces
There are many Android stores now.
See the list below.
For any of these other than Google Play (or whatever comes pre-installed on the device), users will have to enable "Unknown Sources" in the Settings app, which comes with a security warning. Google does a really good job of vetting apps for security problems; it is not known to what extent these other stores do so.
To get your app into one of these, start with the consumer site listed in the URL, and look at the store and see if you want to be associated with it. If so, look around for the "developer" or "partner" or "publisher" link, and sign up.
This list will always be out of date, but updates are welcome. A web search on 'alternative android market' will find lists that include some smaller/newer app stores.
A most comprehensive list can be found at http://alternativeto.net/software/android-market/