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'.
It is increasingly less likely that transactions which don't include a transaction fee will ever be mined. Thankfully! Thus, these spams (or tags or whatever) are generally not going to appear persistent to most people's clients. Without including a transaction fee, a guy with 1 BTC can send out millions of these on the network. (They would not be using the reference software to implement the protocol of course.)
An interesting thing here is that just because one client eventually shit-cans transactions which are not confirmed doesn't mean that every client does. It's a setting. And I could imagine it being quite trivial to code things such that '1enjoy' and '1sochi' associated non-confirmed transactions are never discarded. Thus, they just hang around as a tag on a particular address for anyone running the modified software to use. That is why it strikes me as a light-weight and unobtrusive tagging system which leverages the Bitcoin network itself as a propagation mechanism.
I'm not 100% sure of my assertions here so I would welcome a second opinion on how some of this stuff works.
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).