I like cards, but how I use them isn't very random. Instead I use them in ways that combines randomization with strategy.
Playing cards and tarot cards allow an element of strategy, of bluffing before revealing your choices. They allow reshuffling or re-ordering. You can combine multiple decks if you need more cards, or remove cards to create a smaller deck. They may be used multiple ways because they have suits and numbers. For my game Terribly Beautiful I set the major arcana aside for an initiative system that didn't need a tiebreaker mechanic. With other games (Metropole Luxury Coffin) I devoted special abilities to face cards, aces and jokers. I could go on and on, but you get the idea.
As for randomizers, I like twelve sided dice. They just feel so right to me, round but not too round. When I design with dice I'm always tempted to design for 12-sided dice.