As a long time observer of the database market with no skin in this particular game, in terms of regaining market momentum it is difficult to get past the reputation of being technically defective once that perception is broadly in place. To make matters worse, needing to completely replace the storage engine with a proper design will be viewed by some as an admission of that rather than an upgrade per se. It may be too little, too late for its long term prospects. By contrast, PostgreSQL is doing great right now; just about every company I talk to is using it somewhere.
Putting on my database engine designer hat, MongoDB did need to start from scratch with that storage engine; the original one was a naive design with a lot of problems. The sharding/replication design is still quite dodgy, which will hinder practical scalability. A new storage engine is a start but not enough if MongoDB wants to regain their momentum.
* SQLite - it's everywhere thanks to mobile phones.
* Oracle.
* Microsoft's thing has to have a big following.
* Mysql.
* DB2 is not as big as Oracle, but IBM isn't some lightweight, either.
MongoDB gets talked about a lot, and probably used among people trying new stuff out, but I think a lot of mostly silent people wouldn't touch something like that for their important data with a 10 foot pole.
and browsers...and tons of other pieces of software
SQL Server is definitely one of Microsoft's best products - as well as being an excellent database engine it also is used by SharePoint, the various Dynamics applications (CRM & ERP) as well as being the "natural" choice for application development in .Net
If I had to guess I would suspect that, at least in terms of revenue, SQL Server probably tops Oracle and DB2.
MySQL is most likely the most deployed thanks to the LAMP stack's proliferation across all sorts of small and medium sites. After that it really would be a toss up between MS-SQL who has traction in the SMB space due to it being used for sharepoint and exchange, and PostgreSQL
but lets be honest the most utilized database is Access.
http://db-engines.com/en/ranking_definition
It's kind of how I did http://langpop.com/ back in the day (subsequently sold and it looks like they don't maintain it).
I'd actually say that its feature set relative to other equally stable open-source DBs has gotten worse over the years, not better. Not because its gotten absolutely worse, but because other open source databases have gotten better faster.