Super Mario Bros. 3 had so many innovations.
It's Item Box is amazing. It lets you store items for later use.
Some items you use in levels, and some are specific for using on the overworld map, making the map even more interactive.
Items could be snagged in levels for immediate use, or grabbed from a Toad House.

Mushroom

The most famous Mario item. Was the first item he could get in the first and third SMB.
The mushroom makes Mario grow from small to big.

Fire Flower

Another classic Mario item. This was one of the few items in the first SMB, and carried over to SMB3. This flower allows Mario to shoot fireballs on command. Can defeat most enemies.

Star

Yet another classic Mario item originating from the first SMB.
The star makes Mario invincible for a short period of time.

Leaf
    
This item was created for SMB3. It turns Mario into a Raccoon, which allows him to fly!
The leaf is a fairly common item in SMB3.

Frog

"Ooooh! A Water Level!" - Derrick Naslund
My friend said that to me once, made me laugh. He loves water levels.
So I'd imagine he'd love the Frog Suit, it allows Mario to swim gracefully in water levels, and hop around in non-water levels.
The frog suit can be picked up in Toad Houses in World 3, as well as in a few levels.
(It can also be found in the hidden area at the end of World 2)

Tanooki

Gotta love this item. Gives you all the abilities of the Raccoon Suit, plus the ability to turn into a statue for a few seconds. This item shows up in World 5 Toad Houses, as well as in a few levels.

Hammer Bro.

Admit it, seeing those tough Hammer Bros. in the first Super Mario Bros. made you want to have their ability. Well now you can! This suit shows up in World 6.
In the NES version of SMB3, it was hit or miss getting one in the Toad House, it was a little tense, hoping you'd get one. Made it more exciting when you did though.

P-Wing(Paratroopa Wing)

You look like Raccoon Mario, but have unlimited POWER! You can fly, fly, fly.
You also get a snazzy "P" on your overalls on the overworld map.

Musical Note

This item effects the overworld map. It plays a lullaby that puts the Hammer Bros. asleep.
It allows you to pass them, instead of fighting them.
I never use this anymore, but as a little kid, the Hammer Bros seemed daunting.

Jugem's/Lakitu's Cloud

This is a pretty cool item. It allows you to skip a level. You float right above the level on the map.
BUT! If you get a game over and are sent back to the start, you may have to do the skipped level.
My favourite level to use this on as a child 7-4.

Hammer

I love the Hammer item, can't get enough of them. They allow you to crush boulders on the map.
This let's you take shortcuts and enter certain areas, like the boat area in World 3.
Without a hammer you can't go canoeing, so thank you Hammer.

Whistle

You can grab these a few times in the game, twice in the first World.
It allows you to travel to The Warp Zone. Which allows you to quickly get to any world.
(Except World 1)

Anchor

This is probably the rarest item in the game, as well as the most unknown.
I didn't know about this item until I was older. It is found by accessing a White Toad House.
White Toad Houses can appear once in each World by collecting every coin in a certain level. Level 4 on World 1 for instance.
Not all White Toad Houses contain an anchor. World 1 does though.
But what does the anchor actually do? You can use it to stop the flying airships from flying around the map if you die while playing an airship level. Especially useful in World 5.

1-Up Mushroom

I had to include the 1up. This item pops up in various levels. Grab it to get an extra life.
This is the fourth item returning from the first Super Mario Bros.