Sure you can spread out your money across many addresses but at some point they are going to merge at least a bit again when you want to make a payment. Unless

Sure you can spread out your money across many addresses but at some point they are going to merge at least a bit again when you want to make a payment. Unless you split the money in big enough chunks to make payments from them. Example: you have 10 BTC, spread it to 3 addresses (A: 2 BTC, B: 5 BTC, C: 3 BTC) and want to make a payment over 6 BTC. Now you will have to either create a new address which gets money from B + (A || C), then transfers it to the seller or transfer from said combination directly to the seller. Since one can see B and one other address working together, one could assume they both belong to the same owner. This is just one example of how you can still track address owners with varying chances of success. One can with great care probably make Bitcoin anonymous but the average user wont.