I don't recommend Candyland or Chutes & Ladders to anyone unless the kids they play with are just trying to learn their colors or practice counting.
Monopoly is fun, but I've found kids like it better if you play with some house rules. I recommend dividing all the numbers by 10 and rounding. That makes all the numbers more in the range that kids are used to. I also recommend that you play auction style (where when anyone lands on an unowned property that all players bid for that property). I also recommend that you play instant monopoly (where a player gets all of a color when they buy any 1 of those properties). These rules make the game a lot faster and more fun for kids.
Checkers is a great game for kids, and doesn't really need any modifications other than maybe having the adult play without all the pieces to balance things out.
Other games that are good for kids include:
Blokus (my kids have played that since they were really little, and it's easy to get at Wal-Mart)
No Stress Chess (my kids have played this since they were really little, and it's a GREAT way to learn)
Ticket to Ride (when my kids were really little they played without the missions, and they loved it)
Shadows Over Camelot (although this is a harder game to learn, you can help them a lot since it's Co-Op)
Guess Who (it's pretty basic, but the kids like it)
Parchesi/Sorry/Trouble/Aggravation/Sliders/etc. (these are all basically the same game, and kids like it)
Mancala (my kids have played this since they were really little)
Connect-4 (another one that they've been able to play forever)
