I gave a talk a few months ago, and one member of the audience made a particularly insightful suggestion. My advisor and I are still working on this topic, and it seems like our research is heading in a direction where his suggestion may end up being incorporated into our work in a fairly significant way. We haven't spoken to him about this work since, but how should we deal with this? Should he be an author, or only mentioned in the acknowledgments?
You should at least acknowledge the person who made the suggestion.
I would also ask this person if they would be interested in working with you to coauthor the paper. If the person who made the suggestion is very senior or doesn't work in your area, then they'll likely be happy with the acknowledgement.
However, a suggestion like this, without any further involvement in the writing of the paper isn't by itself sufficient to merit coauthorship under guidelines such as the ICMJE guidelines for authorship.
At present, I don't think merely having a helpful suggestion, even if it launches a fairly significant line of inquiry, merits a paper authorship. They haven't, after all, actually worked on the paper.
This kind of thing is exactly what the acknowledgements section is for. And in several cases, I have thanked colleagues for contributions that were the result of something like this - a helpful comment, a directed question, a conversation over drinks, etc.
It may however be worth reaching out to them to see if they would like to work on the paper with you, if it is not yet fully finished. After all, they were extremely helpful once, they may very well be so again.