Granted, many of these ideas can be restarted by the writers at their discretion (it's their show). So I'm not saying these storylines are gone forever...
First, the original concept of the Lost mini-series/tv movie (which Jack dies partway through) - wasn't the island a Nazi experiment location gone bad? I can see how this changed to the Dharma group as the show was developed.
Many times the writers were aiming the story towards a "choose sides" story (a la The Stand) - Caves/Beach, Black/White, Army/peace-lovers, etc... Part of the choose sides storyline led to the introduction of new characters. I believe this would have been an excellent storyline to use if the show was not doing well in the ratings and they wanted to end the series at one season. It was most likely dropped as they got word of a renewal.
We all know about the Jack/Ana/Kate/Sawyer love story - too bad people didn't like Ana's character. And speaking of Ana, where's the "army" idea that fizzled? Another good storyline for perhaps a 1/2 season and perhaps a cliff-hanger. It's regrettable that most of the tail section got killed off or had to leave the show.
How about the two (or more) sets of "others" storyline. You know, the barefoot savage child-stealing others, versus the boat/gun/hatch owning others. Which is good, which is bad. We'll never know, as that idea has been dropped as well. The writers tried to cover it up with the whole "the others were wearing costumes" bit, but a big deal was made to show that they were different somehow (different agendas, different lifestyles). These differences were meant to match the different stations (science, nature, etc).
How about the "wrinkle in time" story? The pirate ship, the very old bodies (Kate and jack), etc. Most likely an idea saved if the writers needed to end the series quickly - they could "flash foward" to see that only Jack and Kate survived the trials of island life.
And Libby? How great would it have been if she was really an other, a Dharma member or even stalking Hurley for his money? Yes her story can still be told via flashbacks, but I'm sure she was going to be the opposite of Ana's character.
How about the Boone/Shannon love story (ick)? Too bad Standards put the kabosh on the (step)brother/sister love. They just couldn't kill Boone fast enough to get rid of THAT storyline. How much impact this would have had on the overall plot of Lost is unknown, but Lost was mostly about conflicting characters and hidden secrets (at it's basic level).
Feel free to add more I missed, or expand on the above.



