Yes a self employed individual can open a 401(k). This is often referred to as a Solo 401(k). In reality, a Solo 401(k) is just a normal 401(k) plan, however you are exempt from certain testing and filing requirements because you do not have any staff.Here is a quick breakdown of the most popular options:IRA - lowest contribution limitsRoth IRASimple IRA - slightly higher contribution limits. Allows for employer contributions.SEP IRA - very popular for self-employed business owners who want to contribute more than the IRA limits, but do not want to contribute more than 25% of their earned income.401(k) - popular for business owners who want access to a Roth 401(k), want to contribute more than 25% of their income, or want access to additional features such as in-plan loans.