Apparently, cygwin’s distribution of Python 2.5.1 doesn’t come with sqlite3. This is a pity for those who would like to work with Django using cygwin Python.
Building _sqlite3.dll on cygwin is not too difficult. If you are in a hurry, heres the download _sqlite3.dll.
Prerequisites

/bin/cygsqlite3-0.dll
/bin/libpython2.5.dll
/usr/include/sqlite3.h
/usr/include/python2.5/Python.h [et.c]

tar jxf Python-2.5.2.tar.bz2 Python-2.5.2/Modules/_sqlite/
cd Python-2.5.2/Modules/_sqlite/
gcc -shared -o _sqlite3.dll -I /usr/include/python2.5 -L /bin [...]