Lanefan
Victoria Rules
Colour coding can be your friend there - only get green d24s, for example, yellow d16s, and so on. I don't at all mind dice of different numbers than the usual six (4, 6, 8, 10, 12, 20).I don't like using dice like DCC - most of them look similar to existing dice. For example, you might accidentally pick up a d24 instead of a d20.
For any dice of any shape, though, they have to be able to pass a chi-squared test without being given the answers; and I've seen some non-standard dice (d5s in particular) that failed this step miserably.
EDIT to add: if your game is going to use non-standard dice they'd better be included in the box. Not everyone has easy access to getting them otherwise.
I also generally don't like symbols on dice that replace numbers. If the die is entirely symbols and is used often enough in play that everyone soon comes to know what the symbols mean, then fine; otherwise no thanks.I also don't like dice without numbers, like the Star Wars dice. It requires remembering strange runes and patterns that have no bearing in real life. "That comet means you get a special success, but two squiggles means you get two complications that are better than failure and worse than Despair - which is represented by the circle with a line through it on the yellow die."
Even worse are promo dice of regular shapes (d6, d20, etc.) where one of the numbers has been replaced by a logo, as there's no historical consistency as to whether it's the highest number or the '1' that has been replaced.
As for cards, I'm not a fan of them as a full-time resolution mechanic but once in a while (e.g. if a D&D party meets a Deck of Many Things) they can be great.