Muneraven made a comment about cutting material in comments and when I started to answer I realized it really deserves a front page post. Doug beat me to some of it, but I think there's more to add.
Cutting's always hard. So how do you go about it.
First, what Doug said. Anything that doesn't serve the story's core has to go and what the core is will vary by writer.
Second, cut big. The best lesson I ever had on that was in my first short story sale. Everyone in my writers group at the time agreed that the first half of the story was outstanding and that the second half was good, but that they didn't belong together. I ended up throwing away the ending (it's still around here somewhere) and writing a new one. It taught me to be brutal and cut big chunks where possible rather than nibbling around the edges.
Third, time and emotional distance help. One of my stories has sold to at least one nice professional market that paid me in advance before they folded and didn't publish it. That story was 8,000 words the first time out, but my writers group said it was flabby. I didn't see any flab, so I sent it out after making some of the other changes they suggested. No sales for one year and I didn't look at it at all in that time. At the end of the year I looked it over (annual review is something I do this for all shorts when I'm working the short markets). They were right. It was flabby. I cut 4,500 words and started sending in it back out. Got a few nibbles that said it needed some more motivational work for the characters. One year later I looked at it again. Added in 2,500 brand new words that covered some of the same ground the missing 4,500 had. Sold it to the next market. If you can't figure out where to cut, put it aside and come back to it in a year.
Fourth, sentence origami. My friend Mike Levy coined this phrase to describe taking sentences, sussing out the core meaning, and then refolding them to say the same thing with fewer words. I got rid of about 12,000 of the 18,000 words my editor wanted me to cut from WebMage that way. It can work wonders if you're careful, brutal, and diligent. About 1,000 of the words I chopped out of the short mentioned in my third point above went this way as well. Here's an example from a real story that was bought with the first version and published with the last: So I nodded my head in assent became So I nodded my head and then, I nodded.
Does anyone else have any suggestions for chopping the appendages off your darlings?