Two truths about handling criticism:
Truth #1: One of the BEST things you can do as a writer is to heed criticism from others.
Truth #2: One of the WORST things you can do as a writer is to heed criticism from others.
Well, which is it? The answer depends on who those "others" are. In my experience, the people to listen to are those who have a specific sense of what your writing is like when it's at its best. That is, their criticism is not geared toward turning what you've written into "their kind of thing" but rather is committed to helping you make your work what it is trying to be. The very best workshop leaders have this gift--as do the best writing partners and editors. Listen to them. Listen even when the truth means lots of work for you. Listen even when they suggest that you axe that last paragraph you labored over. Listen even when it hurts. Listen.
What about Truth #2? Why is it so dangerous to listen to some (even well-intended) advice? Sometimes the feedback you get is not about doing a better job at what you are trying to do. Sometimes it's really about a reader suggesting that your work should do something other than what it does, that your project should be other than what it is, that you should be other than who you are. (Full author disclosure: this is why NOT to read amazon reviews... one reader rejected What Can't Wait because it was YA and not sufficiently "literary" for him or her.)
There are a lot of responses that fall somewhere in between that of the ideal reader and that of the rejecting reader who wants your romance to be a thriller or wants your literary short stories to be genre horror. But my point is to trust your instincts and, above all, to take the time to develop a sense of your own purpose for a given piece of writing. Weigh feedback carefully against that vision, and work relentlessly to learn from comments that will help you achieve it.
Don't disregard the rest, but handle it with caution. And when it comes to crippling, cutting comments, do your best to be like a duck letting the water (or the criticism) roll off your back.