Bike thieves! commence fist-shaking.
We have free, voluntary bike registration with the local police department where I live in California, mainly for helping return stolen bikes to their owners. I'm not sure how effective it is, and I hope I never have to find out.
Last year, I registered the bike I used to go around
Shikoku at the bike shop I bought it from. It was relatively painless and it felt good to have the bike registered in my name, to minimize the hassle in case I got stopped (which never happened).
In Nagoya, a friend of mine has had his bike (just a little old fold-up, nothing special) stolen from in front of their office a few times; once it was found near the train station and the other time the cops caught a kid riding it. In this case, having the bike registered is what got it back to him. Not sure if the kid experienced any consequences...
A friend living in Ehime was telling me that it was almost expected for your mama-chari to be snagged by some kid or drunk salaryman and either end up abandoned somewhere or at the bottom of one of the rivers after a joyride. It's a crime of convenience, and the country is choked with cheap abandoned bicycles because of it. Mandatory registration doesn't deter any of this behavior, it seems.
Back in 2007 in Tokyo, another friend was riding with me on the bikes left by prior tenants at the temple he was living when we got stopped (my precious story about how I got racially profiled). The bike he was riding was still registered to the previous owner, who no longer lived in the country. They almost forced him into signing a confession that he was in possession of stolen property, for a bike left behind (with the key) by a former student that forgot to transfer registration to the temple. The priestess had to get involved and the cops ended up keeping the bike. So in this case, the registration actually facilitated the
authorities stealing the bike.
So... bike registration has some benefits, and also some drawbacks at times