I will be getting the New 3ds and I was just wondering if it was possible to download my eshop games onto my new 3ds without having to do the system transfer. Because my games are linked to my Nintendo Network account can I download them off the eshop onto my new 3ds and be able to play my downloaded games on both my old and new 3ds? I don't want to do the system transfer because I want to be able to play games on both systems and I don't want to delete all of my games. Also most of my games are downloaded on an SD card.

It's not possible. You must perform a system transfer.

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Fantastic, na magic!

and you are only allowed to connect one 3ds per nnid (is that the right way round?) unless you transfer, then your nnid is transferred to the new 3ds

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NNID/Tumblr/Twitter: Turtlemma
woomy

So I can't even disconnect my Nintendo Network account from my current 3ds and then connect it to my new 3ds?

I'm afraid not. The Nintendo Network ID system is truly awful. Not only are you restricted to one of your consoles but that console is then forever locked to one locale/currency, heaven help you if you ever plan to move abroad, and if you remove the NNID you lose all your games and purchases.

System transfer is your only option.

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Fantastic, na magic!

Wow that sucks so bad. I have had my Aqua Blue 3ds since May 2011, I have over 60 games downloaded on it and now it will pretty much become a $350 paperweight.

A second 3DS is not a paperweight. You can StreetPass yourself and play the StreetPass games again, or get extra stuff in regular games that support it. You can bring both out into a crowd (or to a Nintendo SP relay) and get double the StreetPasses. You now have in-person multiplayer with Download Play.

I first had two when I upgraded to an XL, but if I'd known how much fun it was to have two I would have bought an extra one sooner.