What's the best way to invest money, while at the same time optimally sheltering your income from taxes?

Please provide specific companies, funds, or other investments if possible.

Your 401k and IRA are both designed for tax sheltered investing. Currently you can invest up to approximately $20,000 using both of these vehicles. After that your options become very limited Tax free municipal bonds are a possibility but generally tax free or deferred investments have a significantly lower return than other types of investments. You don't have a choice in what company manages your 401k. For your IRA or other investments I would suggest getting a financial planner. I use Raymond James because they don't have funds or investments of they're own they are strictly advisors so you don't have to worry about them pushing into their own companies fund because they have a quota or are getting a high commission. You need someone who has you best interest in hand and the more money you have the more money a company like Raymond James makes. Other companies like The Principal for instance manage the funds they are peddling so they aren't as concerned with your net worth, they're main goal is to exact as many fee's from you as possible.

Open an Investment account in a bank in another country that has no taxes (Dubai)

Become a loan shark.
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401k and IRA's are great.
just remember that if you have someone else help you manage your money, they're gonna take a cut.