This is both good and bad. This is good because the blockchain is immutable, where for the first time in history we have a global public ledger that cannot be changed. History cannot be rewritten. This is also potentially bad for those of us who believe in privacy. As we know, the blockchain is open so anyone can look at it. And bitcoin transactions although are not on the surface linked to our identities, they are through our transactions and our history. At some point you may have purchased bitcoins through an exchange, or made a purchase online with the bitcoins, etc. These transactions open our real identities to the world through blockchain analysis.
General
The purpose of this post is to ask the community, what are the best ways at keeping your identity private on the blockchain. This isn't about generic user privacy on the web or general security practices. I'd like this post to cover specifically transaction privacy; the best ways to accomplish this.
Bitcoin wallets
What bitcoin wallets are made best suited to protect our bitcoin privacy? There are many bitcoin wallets on the market currently, by my count there are upwards of 75+. Not all bitcoin wallets are treated equally. Some are focused on user privacy. Some stick out such as the infamous Dark Wallet, or more recently another wallet that has been making some headlines is Samourai Wallet. Another wallet provider who says they are pro-privacy is Airbitz. However at the end of the day, are "private conscious" wallets enough to keep our transactions private? Should multiple wallets be used to help keep our transactions private? For example, should you have a "business wallet", "personal wallet", etc?
Bitcoin mixers
Unfortunately, because the blockchain is such a buzzword this year and inevitably next year, there are a whole slew of new blockchain intelligence organizations coming out with one thing in mind - to mine the blockchain and get our data - and use it to fit their business model. Some companies stick out such as Coinalytics, Chainalysis, and others. These companies do not have your privacy in mind. They want your data and want to make a profit off of it. Are bitcoin mixers the answer? There are several bitcoin mixers on the market. If you aren't aware, a "mixer" or "tumbler" is simply a tool used to mix your bitcoins with other people in the attempt to obfuscate your transactions in the attempt to make them private, even to prying eyes that may be scanning the blockchain to put all the dots together. Some mixers are modeled off of the CoinJoin implementation by core dev Greg Maxwell.

CoinJoin by Greg Maxwell
The problem with mixers is that we don't know if they trustworthy? Many of these mixers are products of the dark market where people wish to tumble their coins to hide their dark market transactions. Some of these mixers are only available through the dark web via Tor. As mentioned there are several, such as BitBlender, Bitcoin Fog, Helix, and more recently JoinMarket. Even Blockchain.info has it's own mixer called SharedCoin (over the clearnet). Outside of the trust factor, do these solutions actually work though? I've personally tried BitBlender and can say that the transactions going and coming back out are not linked to my identity. However, do I trust them with larger sums of bitcoins and not to steal them?
I've even seen suggestions to use services such as Shapeshift, where you can convert your bitcoin to an altcoin and back, in hopes that when you get your coins back they are not the same. Shapeshift has said it themselves this will not work, as the coins are held for a period of time and chances are you will get the same coins back. However, proponents of the altcoin Monero claim that the coin algorithm is so privacy-centric that when you convert to Monero and back, your coins you get back will always be different. Unfortunately I don't know enough about Monero to speak about it. Does anyone know how well this would work?
Conclusion
It's up to us as a community to figure out the best tools and help each other, for those of us who care about our privacy on the blockchain. I've posed a few questions here that I'm hoping people can kick around and help answer. It also could be that I'm not asking the right questions, so please chip in and ask or answer away!