UPDATE: Regarding the recent 3DS banwave

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It appears that users are being banned from 3DS online services, en masse. There's no direct cause right now, and seemingly no linking factor. This post is meant as an announcement for users, to be wary, and that GBAtemp will keep you updated as soon as more info rolls in. If you have been banned, please post in the thread below, and we will try to keep tabs on the situation. To be extra sure, it can't hurt to turn off your 3DS's wireless capabilities, so you might as well do that for now.

Edit 1: it appears that e-Shop access isn't restricted if you are banned.

Edit 2: A caller to Nintendo reported that the company said this ban is due to "unauthorized software usage".

Edit 3: @LinkSoraZelda is collecting info. Contact him if you are banned.

Edit 4: Click and fill this out if you were BANNED.

Edit 5:

Thanks to @Joom

Edit 6: Aurora Wright is taking another poll here

Edit 7: Not a lot is known but

There are bans happening, they are happening in all regions.
All models in the 3ds family seem to be candidates for banning.
There is no indication they will be anything other than permanent.
A game or DLC may end up being a cause but there is no one game or DLC that ties banned users together.
The cause or causes are as yet unknown, though it does seem to be related to modifications. Reports of unmodified consoles being banned are as yet unproven.
The banning is tied to something you can modify, thus you can unban. Doing it while the causes are unknown is likely only going to burn a working token though.
There are semi public tokens out there, Nintendo knows how to browse a forum as well as you so don't be surprised if they also get banned.
It does not seem to be limited to a given base firmware version, it does not seem to be limited to any one custom firmware type. There is some speculation that older hacking methods are not being hit as hard but nothing to confirm this yet.
The data collection could have happened this morning, or it could have been months in the making.
A simple check to see is checking your friends list, by itself it will not ban you.
Some are turning their wifi off. It is doubtful this will be of much use and being banned does not seem to come with any downsides that wifi being off will not also mimic.
You may have escaped a ban thus far but it could happen at any point. It could be that they stop in the future, it has happened on other consoles, but you would be living in hope rather than any particularly well founded logic.
The bans are done on the side of Nintendo's servers rather than your 3ds so there is also that.

If you hack your devices/games then their online functionality may be troubled. This has been known for decades, Nintendo seems to have finally caught up with that.

Please continue to share information with the thread or the links in previous edits.

Update 5/30

HOW TO HELP AVOID BANS (we think)​

If I was to guess from the information we have gathered since the ban wave, it seems likely that they are looking for TitleIDs that don't exist. Homebrew shows up in the activity log as the Download Play app, and fake CIA's show up as just ??????. That last one is what I'm guessing they are looking for.

If you are not banned yet or before you unban yourself, go into your friends list, choose settings, and turn off the option to "show friends what game you are playing." This will prevent you from playing games online with friends, so turn it back on when you wanna game with someone, but ALWAYS keep it off when running custom CIAs. Next, go into system settings -> internet settings -> spotpass, and turn off BOTH options. One is auto download software, the other sends system information to Nintendo. Also, make sure you don't have your favorite title set to something stupid like FBI or any other non-Nintendo CIA.

Its VERY likely that these options are what tipped off Nintendo, but we aren't 100% certain yet. The amount of banned people that had one of these options turned on was over 80% for each. If I was to assume that some of those people overlap, its very possible (but not confirmed) that 100% of banned people in the survey had at least one of those options turned on. I personally had all of them off and I have TONS of reasons for Nintendo to ban me.... yet I am not banned (yet).

Another bit of advice: Only run custom CIAs when offline, and after you close them, run a "legit" game like Smash Bros. or something before shutting down or going back online. This way your most recent title won't show up as a fake CIA

Current Theories as to what causes a ban
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* SpotPass Settings: 8 users out of 46 users that were banned have SpotPass completely shut off, or SpotPass only (no friends list visibility)
* Firmware Version (Luma, Nintendo): Literally all reports ranged from 10.2+, I can get exact numbers for this if you'd like, but all firmwares were affected.
* Firmware Type (A9LH, B9S): 44 of the 126 B9S users that answered were banned, pattern was mirrored for A9LH users as well.
* Homebrew Titles such as FBI, HBL, Luma Updater, Themely, and freeShop: Literally about 98% of users both banned and unbanned had some combination of these applications installed. However the common ones were: FBI, HBL, LumaUpdater and NTR.
* Save Modification: Equal amounts of users on both sides have reported save modification in some form, either with PKSM or another save editor
* System Transfers: 188 users said that they had not previously system transfered, 61 of those users were banned; 16 users said they transferred from a hacked console, only three of them received a ban; 13 said they transferred from a stock system and likewise were banned. The rest of our sample did not answer this question.
* Activity Log Information: A majority of those who have not been banned have said they had NOT cleaned their activity logs. I can get exact numbers for this too on request.

This information is just what I've found. Like I said, there could be variables or things we haven't even checked for yet. But these are things that I feel should be disproven, at least with the current dataset we have.

• From the information that we've gathered from some people that have used a packet sniffer such as WireShark, the following data is sent to Nintendo's online gaming servers as soon as the 3DS connects to the internet:
  • Amount of time spent online (timer stops when either the system is disconnected from the internet, or connection drops out, then starts the timer again in a new session when it reconnects to the internet).
  • The game being played and amount of time spent on it during that session.
  • The console's unique hexadecimal ID used in the LocalFriendCodeSeedB, along with it's RSA-signed signature.
  • The console's serial number in which is broadcasted from the SoC and is hard coded in the SoC.
  • Friend Code generated on the Nintendo 3DS system, if one has been generated.
  • Internet connection status (either online or offline).
  • The Nintendo Network ID, if there is one linked to it.
  • Even if the sending of SpotPass Information is switched off, or even hiding your currently playing games. It does not prevent the system from sending currently playing information to Nintendo's online gaming servers, it only hides it from your friends in your friend list (like being invisible on the forum, while mods and admins can still see you). Why? Because even people without a Friend Code on their system have been getting banned too!

• The following data is NOT sent to Nintendo's online gaming servers:
  • The data from the Nintendo 3DS's Activity Log. Oddly enough, while Nintendo does explicitly state that they collect Activity Log data, they're actually referring to their own server's Activity Log, which always tracks every console's online activity, and keeps a record of them that is stored forever. And is only collected in increments of data through a timer and a currently playing list.
    
  • Games or apps that have not been played, regardless if they're legitimate or not. You only get tracked when you're online and using that game or app.
  • Using games or apps while offline. Even though it is stored on the 3DS console's Activity Log, that data is NOT sent to Nintendo's online gaming servers.
  • Custom Firmware. Though we can't rule out the possibility of them releasing a 3DS update in the future that adds such function to collect MD5 hashes of files and FIRM data and send them to Nintendo online gaming servers (which would also be updated in a maintenance).

• Things that people think what happens with consoles, but really doesn't:
  • "LocalFriendCodeSeedB is transferred to the system upon doing a system transfer". This is false, the LocalFriendCodeSeedB remains on the system and does not move to another system.
  • "The console generates a LocalFriendCodeSeedB upon first startup". Again, this is false, the LocalFriendCodeSeedB is made during the manufacturing process at Foxconn. It is generated at the factory, flashed to the NAND flash memory storage, then created as an account on Nintendo's online gaming server and Nintendo eShop server immediately when being manufactured. It is absolutely impossible to generate a LocalFriendCodeSeedB and be able to connect to Nintendo's online gaming server and/or Nintendo eShop server, even if you knew the RSA generation key for it. You'd end up with Error Code 002-0102 "This console's online services have been restricted by Nintendo" if you even tried (the error can either mean two things: The hexadecimal ID doesn't exist on the server, or the request to access the hexadecimal ID has been denied which in other words... banned). So a LocalFriendCodeSeedB generator will NEVER happen! Because it's not worth doing, if it can't connect.
  • Switching off "Currently Playing" information. Once again, this does not hide your online activity from Nintendo's online gaming server, it only hides it from your friends.
  • Switching off SpotPass. Nope, this too doesn't hide your online activity from Nintendo's online gaming server, it only opts-out of receiving SpotPass data, sorry.

So pretty much the bottom line is, if anyone has been using custom apps and/or titles not installed through Nintendo eShop while online in the past, guess what? You're screwed! And it is only a matter of time before your console's unique hexadecimal ID in the LocalFriendCodeSeedB is banned from Nintendo's online gaming server. This will mean, your console can't access the Friend List or play any online functions in games.

If you have been online while using custom apps and/or titles not installed through Nintendo eShop and haven't been banned yet, that's because Nintendo hasn't caught up to you yet. They're still going through each unique hexadecimal ID's Activity Log on their server, and by Activity Log, I mean the Activity Log on their server, not the 3DS console's activity log. And it will be only a matter of time before you're banned too.

Thanks to @Platinum Lucario @MadMageKefka and @ShadowEO !