If it's not working even when you already have Code Assist enabled, Eclipse's configuration files are probably corrupt. A solution that worked for me (on Eclipse 3.5.2) was to:
Close Eclipse.
Rename the workspace directory.
Start Eclipse. (This creates a new workspace directory.)
Import (with copy) the Java projects from the old workspace.
d3dave's answer is cool. However theGreenGarbage mentioned an issue about it which I too find rather annoying. So here's one that doesn't immediately suggest something after '=' sign and when typing blank space: