According to page 12 of IRS publication 529 (PDF), the minimum a gambling log should include is:
Date and type of wager or wagering activity.
The name and address or location of the gambling establishment.
Names of other persons present during the gambling activity.
Amount won or lost.
In addition, you should keep other documentation, such as W2-G forms and losing tickets. Personally, I keep my log in Excel and always retain W2-G forms and losing sports tickets. The book Tax Help for Gamblers by Jean Scott & Marissa Chien has a whole chapter on this topic.
This question was raised and discussed in the forum of my companion site Wizard of Vegas.
Marissa is on Twitter at @taxpro4gamblers, where she occasionally answers tax questions to followers.