They include, in no particular order:
The Parched Sea, by Tony Denning
The Ring of Winter, by James Lowder
The Crown of Fire, by Ed Greenwood
The Song of the Saurials, by Kate Novak and Jeff Grubb
The Prophet of Moonshae, by Douglas Niles
Elfshadow, by Elaine Cunningham
The Wyvern's Spur, by Kate Novak and Jeff Grubb
The Halfling's Gem, by R.A. Salvadore
The Druid Queen, by Douglas Niles
Azure Bonds, by Kate Novak and Jeff Grubb
Spellfire, by Ed Greenwood
Iron Helm, by Douglas Niles
Viper Hand, by Douglas Niles
Thoughts on which of these are the best ones, and which ones to start with?
Many of those novels are just great. But in terms of stand alone fiction, these are the two I'd suggest reading first.
The Parched Sea, by Tony Denning
Avoid like the plague. It's like wading through molasses; the plot and character development is very slow, to the point where it's easy to feel tempted to put it down and move on to something else.
The Crown of Fire, by Ed Greenwood
Solid read, and useful for an introduction to the Realms, though make sure you don't read it before Spellfire.
The Song of the Saurials, by Kate Novak and Jeff Grubb
Fantastic conclusion to the Finder's Stone Trilogy, one of the finest trilogies in all of FR, if I do say so myself. Great character development, and the resolution is quite satisfying. Of course, you'll want to read Azure Bonds and The Wyvern's Spur before this one.
The Prophet of Moonshae, by Douglas Niles
I suggest reading his earlier Moonshae novels if you haven't already. That'll fill in a lot of gaps which you'd encounter without reading the earlier works. On its own, it's solid enough, though I think it (and its two counterparts) pale(s) in comparison to Darkwalker on Moonshae and the other two Moonshae books.
Elfshadow, by Elaine Cunningham
This is an excellent novel with which to start. Elaine is one of the finest authors in all of the Realms, and this wonderful tale unleashes upon the world some of the most intriguing characters in existence: Arilyn Moonblade, Danilo Thann, and of course, Elaith "Greatest Elf Ever" Craulnober. Plot is very engaging and it is masterfully written.
The Wyvern's Spur, by Kate Novak and Jeff Grubb
Book 2 of the Finder's Stone Trilogy, and perhaps my favorite of those three. You'll want to read Azure Bonds before you dive into this one, but make sure this comes before Song of the Saurials.
The Halfling's Gem, by R.A. Salvadore
This concludes the Icewind Dale trilogy, so put it on hold until you read The Crystal Shard and Streams of Silver. I didn't think this one was as engaging as the other two, but it was still a pleasant read.
The Druid Queen, by Douglas Niles
This concludes the trilogy Prophet of Moonshae begins. Obviously, PoM and The Coral Kingdom are pre-reads, but the prior trilogy by Niles is still important.
Azure Bonds, by Kate Novak and Jeff Grubb
Great novel, and opens up the Finder's Stone trilogy, so this is one of the best choices here.
Spellfire, by Ed Greenwood
One of the ideal "Intro to FR" novels. Not especially well-written, but it's a good way to gain a sense of the FR feel. Read this before Crown of Fire, by the way.
The Parched Sea, by Tony Denning
-A stand-alone novel, set in the Anauroch. I enjoyed it, because of the characters, and the view into Bedine life, society, and culture, but at times, the plot dragged.
The Ring of Winter, by James Lowder
-Haven't read, but it has been recommended by sources I trust.
The Crown of Fire, by Ed Greenwood
Spellfire, by Ed Greenwood
-These two books make up Shandril's Saga, along with the final book, Hand of Fire. I haven't read them, nor do I wish to. I'd personally avoid these books like the plague, as they seem to personify a lot of what people dislike about Ed Greenwood's writing- bumbling villains, overpowered characters, unrealistic conflict...
Azure Bonds, by Kate Novak and Jeff Grubb
The Wyvern's Spur, by Kate Novak and Jeff Grubb
The Song of the Saurials, by Kate Novak and Jeff Grubb
-These three books make up the Finder's Stone trilogy. I, personally, loved the entire trilogy, with the second book, The Wyvern's Spur being my favorite of the three. At times, the books can feel a little dated, and a bit campy, but the story never seemed to drag, and the characters- primarily, the supporting cast- were mostly complex and likable.
The Prophet of Moonshae, by Douglas Niles
The Druid Queen, by Douglas Niles
-Haven't read. If you've read the original Moonshae trilogy, these books, along with The Coral Kingdom, make up the Druidhome trilogy, which is sequel, so to speak, of that trilogy.
Elfshadow, by Elaine Cunningham
-Elfshadow marks the first book in Elaine Cunningham's Songs and Swords trilogy. Elfshadow was enjoyable, but I felt that the other books in the series, especially Silver Shadows, were better. That said, you can't start the series at book two, so you need to read Elfshadow if you want to read the others- and you should.
The Halfling's Gem, by R.A. Salvadore
-The last book in the Icewind Dale trilogy. I prefered this book to the other two in the series, as it seemed a great deal more original than The Crystal Shard and Streams of Silver, both of which, at times, seemed to draw from Tolkien's work and "classic" fantasy a little too much for my liking.
Iron Helm, by Douglas Niles
Viper Hand, by Douglas Niles
-Along with Feathered Dragon, these two books make up the Maztica trilogy. Generally speaking, the Maztica trilogy recieved poor reviews, because the events that unfold within too closely mirror actual history. That said, it does have a bunch of elements that I found enjoyable. If you are interested in Maztica, or Latin/South American History, I'd give it a shot.