> Bob's will leaves everything to Abby. Bob has a brokerage account
> solely in his name with no TOD on the account. Bob then dies. It is my
> understanding that for Abby to get the money, you have to go through
> probate. Am I right about that?

Yes, this has to go through probate.

> I have been told that when you are leaving everything to a spouse you
> can skip probate. I am thinking that is wrong.

You are correct.

This said, in a very small dollar estate (e.g. $20,000, with the actual dollar amount varying state by state), some states allow you to transfer assets by affidavit rather than via the probate process, if the sold heir at all and will beneficiary are the same and there are no unpaid creditors with a claim against those funds. 

New Jersey has [two sets of small estate procedures][1] for estates under $50,000. One is settlement by affidavit and the other is a simplified procedure probate case.


  [1]: https://smallestates.uslegal.com/affidavits-and-summary-administration-laws/new-jersey-small-estates-law/