Connections... Definate spoilers
I own all of these modules, and have played through 6 of the 8, so I might as well offer up my two cents.
Sunless Citadel links to Nightfang Spire links to Bastion of Broken Souls. These are almost direct links. If/when the PCs destroy the Gulthais Tree in Sunless, it frees the vampire Gulthais who goes back to his home base in the Spire, and the Spire's evil is fueled by the heart of Ashardalon, a great wyrm red dragon -- the selfsame red dragon you face off against in the final module.
The Forge of Fury has a quasi-link to Lord of the Iron Fortress. The Forge is Durgeddin's old forge, and Durgeddin is one of the souls captured and forced to work on the Artifact weapon in the Fortress, and the Big Bad Guy in Fortress is Imperagon, one of Ashardalon's sons from mixed mating.
Lord of the Iron Fortress has a link to the Standing Stone. I can't remember his name right now, but the tiefling in Stone is creating a servitor race for... guess who? Why, Imperagon from Fortress, who's going to be using that badass artifact weapon when he tries to take over a world. And Standing Stone has to link to Bastion, because that tiefling's working for two masters. The OTHER one is a baddie in Bastion and if they don't torch the tieflings things they come upon correspondence from this baddie.
Speaker in Stones doesn't reaaaaaly have much of a tie in to anything at all as relates to the overall storyline, except that you'll be meeting more illithids in Fortress and wouldn't it be really -interesting- if the illithid from Speaker gets away in the end and the PCs come face to face with him in the Fortress?
Deep Horizon has absolutely *zero* impact on the overall storyline. Zip, zilch, nada. It's there so the PCs can play with underdark foo. Easily replaced with something else you like better (if you like. It's not a bad module and I do plan to run it some other time).
All in all, it's a very interwoven set of modules with a really nifty overarcing storyplot. My group is finishing up Iron Fortress, then it's on to Bastion, and from there to epic adventures of my crafting.