I made my son a counted cross stitch Monopoly board many years ago, and he still has it hanging in his home office. I like your Scrabble idea, and you could also put in names of family members.
I am in the process of making a scrabble quilt. It has been a process of evolution really, I wanted to make a quilt to start with and came across a competition about quilts with word blocks on to encourage people to touch the quilt, I was also looking into other scrabble things and I wanted a flexible way of making visitors feel welcome, hence the block letter quilt. It took a while and I was inspired by an outdoor tile game of scrabble. Anyway, the process is and will continue to be a long one as it is very much trial and error. The plan is to have a large basic quilt, then a smaller board in the centre. This will be the bag where the letters are kept, with velcro openings on all four sides for access to the letters. Each person will have a velcro fastened flap to hide their letters under. I am making the top at least of fleece and the plan is that it can be used out in the garden as a travel rug/portable scrabble game. I have made all the letters. These were printed with my colour laser printer and freezer paper onto cotton and then sewn onto a fleece backing. I then chainstiched all the letters and straight stiched the numbers.the board squaress are going to be separated using narrow bias binding( I am not going to make each square separately but oversow the double letter/double word squares onto the base board under the bias. My current problem and the reason I came across your post is I am looking for a way to get the letters onto the board. It needs to be fleece for the velcro to stick to the squares. I am going to try printing direct onto freezer paper in reverse and using it as a transfer. I started off doing the letter tiles like that but it was too fuzzy. I have started embroidering all the board squares but it is too much hard work and not a nice enough finished result. If you have any ideas, please let me know.
One quilt show had numerous game quilts in an exhibit. I believe it was down in Des Moines. I was unable to get close enough to see how they handled this situation. Good luck!