Ok, a big thanks goes out to Scott Stroz for this one. I've been using Eclipse for a while now but never needed to do a multi-file search and replace until last week. Turns out it is rather simple, but I had never really noticed the feature before. I figure a quick blog post may help others, and since I know I'll probably forget in six months, it will help me as well.
First, select the root folder in Navigator:
Second, go to Search/File in the navigation menu.
Enter your text in "Containing text" (I entered UDF). Note the Scope. This is critical. It should have "Selected resources" picked. If it is disabled, it means you didn't click in the Navigator first. This bugs/confuses the heck out of me. If you do 2 multi-file search and replaces, it is easy to forget to click back here. It is like Eclipse 'forgets' you had chosen a folder before.
Now, instead of hitting Search, click the Replace... button. Obvious, I know, but I swear I had never noticed it before.
Eclipse will now automatically run the search. You will be given a list of results, and the chance to enter your replacement term.
Just type in the term and hit Replace or Replace All.
So far this has worked perfectly for me. I did screw up one time and forgot to change the value on the "With" field, but that was entirely user error, and not Eclipse's fault. Also don't forget what I said about clicking back in the Navigator before you do the search.