The Droid with the Body Glove case on is .75 in thick. So the case adds .25 inches.
I like the case, I like the feel of it in my hand and I believe that it offers some protection, certainly it adds protection versus most other snap on cases or no case.
It can be difficult to take on and off at first, If you are not cautious putting the case on and taking it off it seems like you are going to pull the phone apart or pull the screen off of the keyboard. This can be quite disconcerting, but once you get the hang of it the case can be taken off rather quickly.
Although, as I said i do like the look and feel of the case, I did read a post by someone with a smashed screen who had the body glove case on. It had been dropped face down on concrete. After looking at the pics and examining my case I can see that the middle of the left side of the case that snaps on the front is very thin and has no support, probably to facilitate opening the keyboard. If the phone lands face down and impacts the screen in this area it will be as though there is no case on it at all. However, I do believe that the case will generally offer a decent level of protaction.
The only other thing that I have noticed is that the front part of the case also intrudes about 1/8th inch into the keyboard making the top row of keys slightly harder to hit comfortably.
All things considered, I would recommend the case, it just depends on what is important to you and what else may become available in the future.