Hi Reid,
I think it is a matter of what you are wanting and where you are in your investing career. Personally I would not accept rent in cash but it really depends on the person and their situation.
Reasons Against Accepting Cash:
1. If you are looking at securing more loans in the future, having a good debt to income ratio will help you secure a loan easier. The banks will be more inclined to give a loan when they see your rents are higher compared to the debt you have financed. Accepting cash and not reporting it will hinder this.
2. You do not have to be worried about being audited by the IRS (peace of mind)
Reasons for Accepting cash:
1. If you are at a time in you life when you are not looking to get anymore loans and want to minimize your tax liability, accepting cash could be a great way to do this.
There are obviously more positives and negative to both sides but those are a couple that hopefully help a little. Long Distance real estate investing by @David Greene is a great source. I just read his book and he goes into the pros and cons to this exact problem.
Best of luck,
-Dylan Mathias