Auto-closing brackets and strings in Eclipse is very useful, but it works fine only for typing new code. When editing, it’s really annoying when you want to enclose some existing string with apostrophes and Eclipse engine enters two marks instead of one.
Great thing about Eclipse is that it’s very configurable. Also search option in preferences dialog is helpful. With these two features, it’s easy to find option to disable code completion for braces and apostrophes. Choose Preferences from Window menu, then with tree navigate to Java->Editor->Typing and untick options in Auto-close panel. That’s it.