Fantastic stay
Believe it or not, this was the lowest priced hotel I managed to find near the heart of DC that was at least 3 stars. Reading reviews, I knew it was going to be a good hotel, and once I managed to find a deal on the price, I jumped on it. I'm pretty sure I got the best deal ever. 
This hotel is much higher in grade than I usually stay in, although the vast majority of my hotel time is for business and thus basic...but this place was fantastic. While at the hotel, not one person ever said the word "no" to me, and even when faced with a fairly negative situation (we had a travel issue, not due to the Madison, that prevented us from going to where we wanted to go), they managed to both soothe me and try to find a solution. I know I am a picky person, but they satisfied every request. As an example, at 11pm at night, on a Sunday, my wife decided we needed a fridge. I could have had one at check in, but she didn't want one. I asked the desk staff, who said they'd see what they could do. 15 minutes later, the fridge showed up. Who has a maintenance man on hand at that crazy hour of the night? The Madison does. 
Our room was clean and fresh smelling every day, which was a great boon to the neat-freak wife, and we had housekeeping check on us several times a day when we were hanging out in the room (and didn't have the DND sign up) to offer us water, coffee, or simply ask if we needed anything. What else to praise? The concierge I dealt with (Tony) several times was not only incredibly knowledgeable of places to visit for a variery of different interests, but very patient in explaining how to get to places which helped greatly. We ate at the attached restaurant, Postscript, several times, usually waited on by Mohammed, and he treated us as if we were the only guests there. I wouldn't hesitate to recommend this hotel to my family for a second. Despite the wife's general unhappyness with a history-packed vacation (for the kids), she absolutely loved this hotel. 
The only issue I had with this hotel was that whomever answers their phones seemed to be angry both times I called. I never saw a person at the desk answer the phone, so this might be located elsewhere. I'd recommend booking it online and never calling.