What different devils fruit are there in one piece?

There are many different devil fruits in One Piece, too many to list. The fruits can be broken down into three groups.

Logia-type Devil Fruits allow the eater to produce, and completely turn into a raw element or substance. They are difficult to fight because of this, though the ability known as 'haki' can bypass their intangibility. Logia users have appeared as solid substances (Ice, sand), liquid (swamp mud, slime) and even gas ('gas gas' fruit, and smoke), as well as energies such as lightning, light and fire.

Zoan-type Devil Fruits grant shapeshifting abilties. By default, the eater gains two new forms they can turn into; the animal that the fruit is named after, and a hybrid between that and their normal form. This normally means human, half-human and animal forms, but there are exceptions. 'Pekkoms' was actually a lion to begin with (he belongs to a tribe of animal people called minkmen), and uses a Tortoise devil fruit. 'Chopper' was a normal reindeer to begin with, and his fruit was in fact a 'human human' fruit, thus his 'normal' form is a normal reindeer, his hybrid form is a little bipedal reindeer, and his 'animal' form is almost fully human. Fleet Admiral Sengoku is human, and ate a special human human fruit which lets him turn into a giant gold Buddha. Lastly certain inanimate objects have been imbued with Zoan devil fruits to turn them into living creatures. Thus 'Funkfreed' is a regular sword, that can change into a regular elephant, and has a hybrid form that is an extending sword with an elephant head.

Lastly there are 'Paramecia' devil fruits. These are basically anything that doesn't belong to the two other categories, and their effects are wide and varied. Some resemble Logias but not fully, because they're either made of/turn into a substance but can't create it seperately or turn into it fully (Jozu's Diamond-Diamond fruit and Luffy's Gum-Gum fruit) or they can make it but their bodies don't consist of it (Mr 3's Wax-Wax fruit and Magellan's Doku-Doku fruit). As well as these, Paramecia fruits have been known to - give control over magnetism, let the user split their body into pieces, emit slow-motion beams, change one's age, change one's face, be able to eat anything and combine things inside themselves, morph body parts into weapons, etc, etc.