High frequency trading (HFT) makes money from tiny changes in stock prices. It's purely speculative - it does not involve consideration of the fundamentals of the companies/bonds involved. Traders "compete on a basis of speed with other high-frequency traders".
I think another solution is a tiny blurring of the prices - issuing quotes with a x% error. Denying HFT firms perfect pricing knowledge prevents their profiting from trivial price changes.
This avoids the major issue with the Tobin Tax: firms can flee to countries without a Tobin tax, or with a lower rate. However, major exchanges (LSE, DAX, CAC) sit in the countries who are interested in instigating a Tobin Tax. These countries could simply impose this price blurring on their exchanges, completely excluding HFT and its possible effects upon money invested there. It doesn't rely on other countries doing the same, and would allow long term investors to choose to stick to the exchanges that ban the practise, with the potential reduced volatility it provides.
Long term investors wouldn't be adversely effected - they frequently invest on the basis of 15 minute old data that already has much larger price differentials than would be required to wipe out HFT firms. Markets are based on trust, so opportunistic blurring free markets would be less attractive for being based in small, less trusted and stable countries. Dark-pools of privately owned stocks would also be riskier, and more expensive.