A couple days ago, NeoGAF uncovered evidence that Nintendo was preparing a browser-accessible eShop. Shortly after that discovery, Nintendo announced that you'll be able to purchase or pre-order select first-party digital titles for Wii U or 3DS right from its website. This isn't quite the full eShop that was previously reported on and tooled around with, but it's most definitely a first step towards that complete online shopping experience.
As Nintendo explains, this service applies to games that have a "Purchase digital" or "Pre-order digital" button on their information page. When completing the transaction, you'll be able to request an email with a download code so that it can be redeemed manually, or you can associate the purchase with your NNID so that it's downloaded on your machine automatically. In the case of pre-orders, you obviously won't be able to redeem your game until release day.
On the upside, you'll be able to use this service to gift games to friends, a feature that was part of the Wii shop but has sadly been missing from Wii U and 3DS. On the downside, you won't be able to use your eShop balance to make online purchases. Hopefully that feature is added at a later date.