For board/traditional games, we like Robot Turtles (easier version of Robo Rally, which you can upgrade to when they are older), Yahtzee, Backgammon, Stun. Yeah, for over 3, but the younger ones like to watch.
And no one mentioned Snap Circuits Jr.!
I found backgamon to be fairly complicated and never really got my kid to play anything abstract, closest I got was with Hive, but that quickly devolved into stacking cute little bugs on hexagons into stacks (not that I am complaining)
It either needs to be fast, reflex games like Hali Gali, Dobble, e.t.c. work well, or with interesting enough theme, i.e. she actually likes to attempt to build a giant sprawl in Carcasone :D
But I will definitely check out robot turtles :)