Connect 4: The only rule was to take turns putting them in; there was no win condition. Just putting the tokens into the slots is/was apparently very satisfying for both my children; with supervision and a binky in place, A. could play with it even when she was still terrifyingly oral. I've always tried to separate the pieces by color and enforce selection from within color. I usually just grab errant hands that are attempting to put a piece in when it isn't his or her turn, and then I say things like, "my turn", "T.'s turn", etc.
Honey Bee Tree: The issue here is setting up the tree. You have to put all these leaves-on-posts through small holes in the hive/tree, prior to putting the bees on top. Little kids tend to want to (a) participate and (b) put the bees in right away. Participation is tough, because of the little holes problem and if you have fine motor issues, it's worse. By definition, littles have some fine motor issues, and my kids have enough problems on top of that to qualify for services. Some days, I think _I_ should qualify for services. And if you let R. participate, he usually turns the whole setup into a system, and that turns out to work less well during game play (which is why the directions say "randomly"). Again, we completely ignore win conditions; the process of removing leaves is quite satisfying all by itself.
Spill the Beans was purchased at the same time for the same purpose, however, it's been impossible to use in a turn taking fashion (at least for me) and hard to communicate the idea anyway. The kids are somewhat fascinated by it as a toy, but I would skip it if I had it to do over again. They may like it as a game when they are older.
Candyland the board game is an old favorite for first-board-game, and it is great for that purpose for neurotypical kids. There is also a candyland game/toy with a lever and colored plastic shape tokens and 4 gingerbread person shaped cards. You take turns pressing the lever, getting a token, and seeing if it fits on your board. Well, that's the idea. We take turns pressing the lever, but we generally do the cards cooperatively, possibly doing all of them at the same time. That is, rather than putting a token back when it isn't on my card, I check to see if it is on one of the other cards. I think T. would probably understand the actual rules, but I have Issues with competition in general, and his instinct is to just put that token wherever he can.
The process was reasonably successful. In conjunction with everything they do at the school T. is generally reliable about waiting his turn in almost any context (altho I don't push my luck, which is why there are two iPads in the house), altho he might need a physical reminder (such as a restraining hand on his shoulder to stop him, or one on his wrist or hand) if something is within grabbing reach.