File extension .DB - What kind of database is it exactly?

Marco Pontello's TrID is a great way to determine the type of any file.

TrID is simple to use. Just run TrID and point it to the file to be analyzed. The file will be read and compared with the definitions in the database. Results are presented in order of highest probability.

Just download the executable and the latest definitions file into the same directory and then run TrID:

trid.exe "path/to/file.xyz"

It will output a list of possible file types for the file with a confidence rating. Here's a screenshot of using TrID to analyze a SQLite database file:

There's also a GUI version called TrIDNet:

If you're on a Unix-like platform (Mac OS X, Linux, etc), you could try running file myfile.db to see if that can figure out what type of file it is. The file utility will inspect the beginning of the file, looking for any clues like magic numbers, headers, and so on to determine the type of the file.

Look at the first 30 bytes of the file (open it in Notepad or Notepad++ or another simple text viewer). There's usually some kind of tag or extension name in there.

Both SQLite 2 and SQLite 3 have a very clear message: "SQLite format 3" for SQLite 3 (obviously) and "** This file contains an SQLite 2.1 database **" for SQLite 2.

edit
Not that encrypted SQLite databases don't have a header like that, since the entire file is encrypted. See siyw's comment below.