I registered on http://Oracle.com in order to download 11g R2 Express edition database. But http://Oracle.com offered me download links only for Windows 32bit and for Linux 64bit.
Is there somewhere 64bit Windows version of Oracle 11g XE database? Are 64bit versions available only for paid Oracle db?
There is
I used this blog post to install it in my machine: http://luminite.wordpress.com/2012/09/06/installing-oracle-database-xe-11g-on-windows-7-64-bit-machine/
The only thing you have to do is replace a registry value during the installation, I've done it about three times already, and every time found a different reference on-line, none here on stackoverflow.
EDIT: as @kc2001 noted, regedit must be run as Administrator, and added this tutorial: (a bit more colorful): http://www.hanmiaojuan.com/2013/03/install-oracle-xe-11g-for-windows7-64bits.html
There is no Windows 64-bit version of Oracle Express Edition. You'll have to go for Standard/Enterprise editions.
I just installed the 32bit 11g R2 Express edition version on 64bit windows, created a new database and performed some queries. Seems to work like it should work! :-) I followed the following easy guide!
Oracle 11G Express Edition is now available to install on 64-bit versions of Windows.
Oracle 11G Download Page
Some of more advanced Oracle database features such as session trace do not work properly in Oracle 11g XE 32-bit if installed on Windows 64-bit system. I needed session trace on Windows 7 64-bit.
Apart from that it works well for me in multiple production MS Windows 64-bit systems: Windows Server 2008 R2 and Windows Server 2003 R2.
It's not available yet. See this thread on the official forum.