Starting with the most popular retirement plan option, the 401(k), your investment options are limited by those the plan sponsor has chosen, unless your plan sponsor has adopted a self directed account as part of their options. Those in the "plain vanilla" 401(k) options usually include stocks, bonds and cash or a money market account. The same holds true for 403(b) plans, but I have not seen a 403(b) with a self directed account as one of its investment choices.
Once you move into self directed IRA's or small business retirement accounts, your options are increased dramatically. The only restriction I can think of in this arena is anything involving borrowing or leverage. Using leverage creates a nasty thing called Unrelated Business Taxable Income (UBTI) which the IRS hates/prohibits.
With the advent of Exchange Traded Funds or ETF's, there is a vehicle for just about any type of investment you want to make in a non 401(k)/403(b) retirement account. While the ETF itself may be traded on a "market", it's the assets underlying the ETF that will guide you to making an investment decision.
Hope this has given you some things to consider further!