I would love to have a "Game Tags" feature that differs from the "Notebook" in a fundamental way. This would be a top-level note/tag for organizing games. People could add a brief note that would show up, perhaps, in their "My Games" list next to the Game Name or in the Info pop-up. Rather than a note to yourself about how a game is progressing, you could tag all of your games of a particular opening, or note to yourself to review and analyze a particular game later. I think having some additional tagging (even if it's just a single text field) would be extremely useful to those players that organize and review their games.
Also, the database addition would be a relatively simple procedure as the field could be added in the same place as the notebook. Integrating with the UI might take a little more thought... perhaps a ajaxy "i" icon where the "info" and "log" links are that would expand that textfield on click and/or a small field in the playchess view. I'd love to hear other people's ideas on this.
At its extreme best, it'd be nice to be able to add custom searchable tags to games, but even a simple editable text field would open up a world of possibilities.
What do you all think?