Update: Sony has increased the availability of its previously suspended PlayStation Network voucher redemption function.

In an update on the PlayStation Blog, Sony offered the following update about redeeming codes online:

We are continually increasing the availability of voucher code redemption functionality. We appreciate your patience and apologize for this inconvenience.

It's unclear if this means all vouchers can be redeemed again, or only certain ones on certain devices. I was able to redeemed a PlayStation 4 download voucher this morning without issue, so it appears to be working there.

[Source: PlayStation Blog]

Original story:

The PlayStation 4 launched in Europe yesterday and the influx of new PlayStation users has made it necessary to temporarily suspend the ability to redeem codes.

The PlayStation Network's other functions, like online multiplayer, are unaffected. A post on the the PlayStation Blog shares some more details:

To minimize the inconvenience we have suspended the “redeem voucher” functionality while we investigate further. Unfortunately this means that money cards, product vouchers, PlayStation Plus vouchers, PS3-PS4 upgrade vouchers and any other vouchers for digital content are not redeemable at this time.

PSN update: http://t.co/5YKoqxntLU Voucher redemption currently down, online play and other features unaffected. Thanks for your patience!

— PlayStation (@PlayStation) November 30, 2013

Sony says that it will offer an update soon.

[Source: PlayStation Blog]

Our Take
I was able to redeem a code late last night, which was after Sony posted this notice online. The service might already be back up, or it might not be down for everyone. Regardless, if you try to redeem a code and it doesn't work, this is likely why.