Do you miss something on BrainKing.com and would you like to see it here? Post your request into this board! If there is a more specific board for the request, (i.e. game rule changes etc) then it should be posted and discussed on that specific board.
Autopass: an option for a player; if this option is turned on (perhaps it can be made configurable per game type, or even per game) the system will play a "Pass" for the player if the player cannot make a move. This may require the system to roll the dice before the player visits the game. Useful for all gammon variants (including Grasshopper) and Ludo.
Automove: similar to autopass, except that the system will move for the player if the player has only one possible move. Handy for chess (specially Anti-Chess and Dice Chess), checkers and variants, Ludo (with both players having autopass and automove turned on, it would be possible that the system finishes the game from start), gammon variants, etc.
A change in the vacation system: instead of giving all the players a years worth of vacation days on January 1, give all the players a small number of vacation days each month (say 1 day/month for pawns, 2 days/month for knights and bishops, 3 days/month for rooks, 4 days/month for black rooks). Vacation days accumulate (so you can save your days you earned in January and February and spend them in March) up to a certain maximum (say the current yearly limits). New players could start with half or a quarter of their maximum. This avoids having a pile of games in the beginning of the year that take a long time to timeout because everyone got a new allotment of vacation days.
Introduce the Glicko rating system. The current rating system considers only the number of finished games as a measurement for how realiable ones rating, and not how long ago those games were finished. Currently, someone who has finished 100 games, 99 five years ago and one 5 months ago is considered to have a much more reliable rating than someone who has finished 24 games, all in the past 7 days. The Glicko system takes activity into account - beside the rating, it tracks a rating accuracy, which increases the more games have been finished, but slowly decreases over time. The rating accuracy can be used to determine whether a rating is established or not (this is what FICS does). The system and its algorithms are in the public domain.
When calculating ratings and determining ratings, a match is currently considered a single game. You can finish 120 rated games, and still have an established rating if all you did was play 5 game matches. Also, winning a match 4-3 gives the same rating change as winning a match 7-0. Not only do matches get underrated in ratings, they also make the white/black win tables on the rules pages far less useful. Consider for instance an imaginary game where white wins 100% of the time, but all the games have been played as 2 game matches. Then the table would show 0% white wins, 0% black wins and 100% draws, given the impression of it being a very balanced game. I think that for certain statistics, an N-game match should be treated as N individual games.
A new time control option: no vacation days before move N (with N settable). This would allow people to have games were they can take vacation days, but avoid having games that no (or a few) moves been played waiting for a time out. This should speed up some tournaments without preventing players to take vacation days at all.
On the page where you commit your move (with the 'move' button), make it configurable for the player to have the move button (and nothing but the move button) right above or below the board. Even with the current "Show move buttons directly below game boards" settings there are the game name, player names, draw offer checkbox, and two text areas before the button, needing one to scroll down a full window heigth. Moving the important thing to the top halves the number of steps you need to take.
With the growing number of games, we probably need some more groups. For instance I would like to see the 'lines' group split into four different groups: Line4 (Line4, Anti-Line4, Linetris, Spider Linetris, Spider Line4) Line5/6 (Five in Line, Pro Five in Line, Swap Five in Line, Connect6), Pente (Pente, Small Pente, Open Pente, Keryo Pente, Small Keryo Pente, Open Keryo Pente) and Other Lines (PahTum, Hasami Shogi, Scrambled Eggs, Lines of Action - although the latter two have nothing to do with creating lines and should perhaps not even be in the lines group; all they have to do with lines is the movement of pieces, but then Amazons could also have been put in the lines category). The Froglet games could become their own category, and perhaps Ataxx and Assimilation as well. Chess is also a large category and could benefit from further dividing.
In Dice Chess, instead of showing the number of pips, show the piece that needs to be moved. The number of pips have nothing to do with the game. And while you would have pips if you were to play this game face-to-face, it's only because dice with pips are common and dice with chess pieces rare. But on BK, we're playing with web browsers and instead of showing an image of 5 pips, an image of a queen could be shown. No need to have to memorize the pips to piece mapping. The dice could be made a configurable option; we can already pick what style of chess/go/checkers, etc pieces we want, adding a "Dice Chess die faces" doesn't seem to much of a stretch.
To speed up game start, in the Boat games, both player should be able to configure their navy simultaneously. From a game perspective, there's no need that the second player has to wait configuring their navy until the first player is done. This is true for other games that need players to set up their boards as well.
An option to automatically reject all invitations. Or otherwise, have the possibility of invitations listed at the bottom of the main page so they can be ignored without being intrusive.