Here are some items I'd like: Character Items! They can be used by any character, but are best with a certain character, like a Fire Flower for Mario. If, say, Fox uses it, it shoots fireballs in a straight line, knocking enemies back and doing damage. However, if Mario uses it, it shoots fireballs in a wide arc, juggling characters and doing lots of damage.
Also, maybe Armor. You pick it up, and your damage counter will be replaced with a health meter, and when you get hit, it takes damage. When it runs out of health, it breaks and you take damage normally. A rare item, slows you down, and makes you fall faster.