Quite simply….any and all!
All IRAs can be self-directed. The key question you need to ask yourself is: 1) Do you want to self-direct your IRA account and, if yes, 2) Do you want FULL checkbook control of your IRA assets? Most people, when they realize they can have checkbook control of their retirement assets, find this to be an exciting alternative to simply using an IRA custodian or administrator.
But, what specific IRAs can be self-directed? They are:
SEPs (Self Employed Pensions); and,
Remember, it is not whether you can self-direct, but whether you want to self-direct.