I have an android phone (nexus s, sdk v15) which shall send a string to a development board running in nfc-reader/writer-mode by using tag-emulation. I know this is not official
For a device running stock KitKat 4.4
With Android KitKat 4.4 the ability to have the phone act as an NFC card is built into the operating system so you no longer have to rely on Cyanogenmod or a custom ROM. It won't let the phone act as a Mifare Classic tag per se but I've had great results in getting my phone to communicate with an ACR122 reader so I'd definitely recommend this option if you can get 4.4 on your device.
If you're wanting to run below 4.4 and are willing to use Cyanogenmod
It is possible to load applications onto your device and have them communicate with a reader via NFC quite easily however you must be running Cyanogenmod, this feature is present from CM 9.1.
Wanting to run on Gingerbread (the old answer)
Yes it is possible and there's been a patch put out there for 2.3.4 to enable it, I'll post a few links for you to have a read of.
They do require flashing a 2.3.4 Gingerbread ROM to your device along with some other patches to enable the card emulation features so if you're not willing to do that then they won't be of much use but as far as I'm aware it's the only way to get it working. I haven't actually tested this myself but user comments suggest it works.
Here is a link to a blog describing the whole process: http://techshek4u.blogspot.co.uk/2012/01/applying-card-emulation-patch-to_03.html
Here is a link to the original forum post with the patch for 2.3.4 to enable it:
http://forum.xda-developers.com/showthread.php?t=1281946
And a link to the original discussion where various developers are trying to get it working, depending on your technical knowledge of Android and NFC this could be more or less interesting: https://groups.google.com/forum/#!msg/android-developers/1fw1qfFqpGc/6dlzvTqExN4J
Caution: According to NFCGuy from his answer "Don't bother with downgrading your phone to GB if it is running ICS. You cannot downgrade the NFC firmware to be compatible again with GB, so NFC will simply not work if you flash your device with GB."
If you root your device, it is possible to create an app that turns on the card emulation mode. It is not too difficult, see e.g. https://stackoverflow.com/a/10506299/1202968.
However, card emulation is completely handled by the Secure Element. Your app has no access to the data that is being transferred. The only way to get control over that would be to create and install a Java Card applet on the Secure Element. However, to be able to do that you need acces to secret authentication keys that are only known to Google.
PS: Don't bother with downgrading your phone to GB if it is running ICS. You cannot downgrade the NFC firmware to be compatible again with GB, so NFC will simply not work if you flash your device with GB.
Host card emulation is now officially supported by Android, according to http://developer.android.com/guide/topics/connectivity/nfc/hce.html