Sara we play lots of games with dice, one dice or two, have done for several months. DS loves it I'm sure Z would love it too. We don't have snakes and ladders yet (it's on the list though) but have played very similar board games from some of his toddler magazines (bob the builder game and such, dice, counting, moving, some spaces say go back or go forward etc).
For some other ideas - we play 2 dice bingo here so I write numbers from 2 - 12 on cards and we shake out 2 dice, DS adds them up and we all cross off the number if we have it. It was DS's idea so I just ran with it.
We also (but not often) do a 1 or 2 dice physical game, I made an indoor assault course with a few chairs and a bean bag etc then lay out numbered cards I made which have an instruction on each card. So you throw dice, move than number of spaces (climbing chairs or crawling through table tunnel as you go) then when you get on your number you follow the instruction, eg no.5 do 5 frog jumps, no.6 do 6 star jumps and sing a song about stars...etc I made it up for days when we couldn't go out but he needed exercise.
We are getting the Frustration from our list too with the lovely 'pop' dice in the dome at the centre of the board (I'm getting the unbranded version which is just like the old Frustration as the new Frustration has some added thing that I think makes the game more advanced or confusing).