I actually got 2 transactions for .00000000 somehow... and when I went to look at it again today both of the transactions are gone! WTF? They were there like all day yesterday, now it only says I have one transaction, but at one point it did tell me I had 3... How weird... Is this being used to keep track of us? Someone sending out .00000000 transactions so they can eventually track all of our BTC addresses???
There is really no mystery here. Someone sent you some perfectly valid (and tiny) transactions. They were signed appropriately and went out on the network. Whatever client you are looking at saw these transactions and added them to your balance.
Eventually these transactions go long enough without being mined (and thus made part of the blockchain) that whatever client you are looking at gave up and decided they would never be 'confirmed'. Thus, they appear
to you to have 'disappeared'.
...
Mine was a local wallet on my computer, and it didn't show up on there. It showed up on my BTC address when I searched it up on blockchain.info. It could be used to run a program, see what all the BTC addresses are, and someone could easily be using a program to check if the address is real or not and keep a record of them all. It's the only thing that makes the most sense(other than spam). Who would do this you ask? We don't know, we can guess, government(they want to tax and regulate good chance).
There is really no such thing as a 'real address'. Any address which has funding has representation in the block chain (else, how did it get funded?), and thus the public address is available to anyone. An address which has never been sent any bitcoin might be considered 'not real', but it's also fairly un-interesting.
In other words, there is no need to spam a wallet to find out if an address is 'real'. The info can be obtained quickly, easily, and cheaply by just parsing the blockchain.
One method of tracking would be to send tiny transactions which
are eventually confirmed then hope that when the user tries to make a spend, this dust is swept up and made part of the spend. This is now expensive because it is not reliable unless the spammer includes a transaction fee (around 5000x the dust value currently) in order to ensure that the dust is confirmed and made permanent.
Client software may try to spend the unconfirmed transactions (like the ones we are talking about here) and it would more-or-less cause the entire wallet to become unusable until the dust transaction eventually fails to confirm. This because a spend often spends
all your money and returns the balance back to your wallet. This issue of is being worked on.
If your local machine is running a 'full client' then it may be listening for unconfirmed transactions on the network and may pick up this spam. Very recent developments involve changes to a local client which treats unconfirmed transactions differently in terms of computing balances, deciding how to construct 'spends', etc. No matter what, software is being used to compute balances, this explains why you see the dust transaction in some places (like blockchain.info which is well connected) and not in others.
Again, these are my own understandings and I am not 100% sure of the exact details so if anyone wants to propose corrections, please do.