I think neither the published order nor the chronological order do the series justice.
I always have recommended the series in the following order:
- I, Robot (some lists omit this, but this is really the "origin" story of this universe - The Complete Robot can be substituted here, since it contains the same stories as I, Robot)
- The Elijah Baley series (which obliquely tells the story of Earth's first robotic forays into space)
- The Galactic Empire trilogy (since these 3 books are unconnected to each other, besides taking place in the same general universe, this series can really be read in any order)
- The original Foundation Trilogy
- Foundation's Edge
- Foundation and Earth. (To me, that is really marks the end of the best of the work, and you can stop there. Or, you can proceed to the later additions to the series, which I find do not hold up as well as the others.)
- Prelude to Foundation
- Forward the Foundation
The reason I like this order is that it preserves the chronology of the **reader's discovery** of the story. Neither the publication order nor the pure chronological order do this - *Prelude* and *Forward* are far weaker entries, and remove some of the mystery the first-time reader would have going into the first Foundation book. Part of the enjoyment of the *Foundation* novel is that you don't know who Seldon is, in those opening scenes on Trantor, or what role he's going to play in the story. If you read *Prelude* and *Forward* first, you'll already have an earful about Trantor and Seldon before you get to Seldon's introduction through Gaal Dornick's eyes in *Foundation*. I'm also completely ignoring the non-Asimov entries, which in my opinion don't add much to the series.
If you've already read the original Foundation trilogy, I'd recommend going back to the other series before finishing with Foundation's Edge and Foundation and Earth.
For those who have already read the books, I could see some merit in reading them chronologically, but for those who are new to the series, I highly recommend ignoring both the publication order and Asimov's own suggestion on reading order.