Monster Hunter 3 Ultimate will allow online play on the Wii U version. The 3DS version, on the other hand, is restricted to local play. But if you reeeeeaaaaaally reeeeeaaaaaaally want to take the 3DS game online, it will be possible through a rather convoluted workaround.
During a Japan-exclusive, third-party Nintendo Direct held earlier today, a solution involving the Wii U and a regular ol' Wii LAN adapter was discussed. By plugging in the adapter and installing a packet relay tool, you can hit the net by sort of tricking the system into thinking you are playing the Wii U version. Unfortunately, you won't be able to play a Wii U copy at the same time (remember, cross-platform play is normally allowed), and you can't create lobbies but only join those set up by other Wii U players. But at least you'll be online!
It makes me wonder why the 3DS game didn't have online capabilities from the get-go. The original Wii version had it as do the Wii U version and the upcoming Monster Hunter 4. In any case, this method has only been announced for Japan thus far, though it doesn't seem like it would be too difficult to release the relay tool elsewhere.
Monster Hunter 3 G on 3DS to Go Online Via Wii U Adapter [Nintendo Life]