You can also type the following in to the command prompt/terminal
If your app package was com.example.dbtest and the database was called sqlite.db
adb shell
run-as com.example.dbtest
cat databases/sqlite.db > /sdcard/sqlite.db
exit
exit
adb pull /sdcard/sqlite.db /path/to/place/file
(if you leave the last parameter blank, it will be placed in the same directory as adb)
This does not require root and be scripted to remove any file from your apps.
You could also use a stream reader and writer to copy it to the sdcard. Do not copy it row by row as barmaley suggested as this may mask errors.