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I thought the talk about salary would come up after call back/offer but in two of my interviews this came up. I said that I did not have a salary in mind yet but that I am open to reasonable offers and flexible, willing to negotiate. How do you answer something like this without screwing myself over or my chances of employment?

You left out of your question whether you're a lateral, first job out of law school, etc., but I think your approach is right. You want them to make the first move. I wouldn't necessarily tell them that you're willing to negotiate as that might lead them to start with a lower number. Just smile and tell them that you're willing to work for the market rate and that you're very interested in receiving an offer from them and you wouldn't expect the salary to keep you from working there because you feel the fit is good, etc., etc. The idea is to turn it into an expression of your enthusiasm for the place without giving a number. Once they tell you what they have in mind (because they have an exact number in mind), you can go from there.

I am a second year lateral (1 year of small firm experience post-grad). Is it ever a good idea to drop a salary number first? Or will "I would appreciate a market rate, but I certainly wouldn't let salary be the reason for preventing me from working at this firm, as I am sincerely interested."

The advice I always hear is to make them give you a number first. In reality, you're gonna either have to say a number or just sound really awkward in your answer. Its not really a terrible reply to say "I am flexible with my salary requirement, and it would largely be influenced by the benefits package and what else the firm offers. Without knowing that its difficult for me to make a firm request of a number. If you're asking me to give you an approximate number, I would feel comfortable with something in the (insert 70s, 80s, 90s, etc.)."