A lot of known glitches
0.00 at Dirt Ring
Phnom Penh suicide
Cars in Tommy's Villa
More cars in a garage
Hands up
Bike Morphing Glitch
Drunk Glitch
Mysterious Ghostworld

Grab a Sanchez (for example from the Trial by Dirt Mission) and drive to the Hyman Memorial Stadion with it. Drive the Sanchez through the open door through that you enter the Stadion event missions. Get down from the bike in there and the mission starts. Well, you should check that the next station event really is Dirt Ring ;).
Now you are inside and there 2 two motocross machines in there. Get onto the Sanchez that has no pink marker under it and collect all the pink checkpoints. Once you got them all get onto the other Sanchez, the real deal with the pink marker underneath it. Now the mission starts and you already collected all checkpoints. So you did the mission in 0.00 seconds and get a lot of money!

This is a funny glitch you can reproduce only at the start of the Ricardo Diaz: Phnom Penh 86 mission.
Drive a motorcycle to Diaz' villa and park the cycle in the pink marker. As soon as the cutscene starts press . Once the scene is over you are still on your bike and not in the chopter, but you are talking to Lance. So drive somewhere from where you can see the helicopter above the house. Get out the rocket launcher and shoot the helicopter. After 3 hits it goes down and you die as you are in the helicopter. Great!

If you try to get into the Villa on Starfish Island with a car the car always disappears. If you still insist on driving around your mansion with a fast car or a bike (who wouldn't like to do that) then this is pretty easy to do:
Get a fast car, for example the Infernus in front of the mansion and drive halfway through the door. This makes it easier to aim. Now drive backwards down the stairs in front of the house and then speed up and drive full throttle towards the door. Just a moment before entering the door you jump out fo your car and there you go, the car drives into the mansion. You need a lot of speed for this glitch so it doesn't work with every car.

This is pretty easy and works the same in GTAIII. Just park one car in the garage. When you come along with the next car, park it in front of the garage, get out, and get into the garage. Get in the car already in the garage and drive is halfway out so that it is halfway inside, halfway outside. Now the garage door won't close anymore. And this makes it easy to park the other car inside the garage and afterwards also park the first car inside again.
But be careful, a garage can not store more than 4 motorcycles. Every additional motorcycle will just disappear afterwards.
You can also use the garage as a cheap repair shop (cheaper than Pay 'n Spray) for your wrecked cars. Just drive a wrecked car into the garage, let the door close. If you get in the car afterwards it is all repaired.

Get the Katana, the Japanese sword. When pressing the action button to strike a blow while you are running Tommy holds his hand up. If you walk onto a pink marker to start a mission like that Tommy still holds his hand up like that. Even when you strike some more blows Tommy still holds his hand up like this.
Also when having the chainsaw selected when receiving the call for one of the assassination missions Tommy looks quite strange on the phone...

You need a motorcycle for this glitch, preferably a PCJ600. Drive you motorcycle to a shop where you can change clothes. Park your bike directly on the marker for the clothes. Get off from the bike and get on it again so that you also change clothes at the same time. Now you are grown into your bike. You cannot fall off from the bike anymore now. To get out of this mutation press .

This Glitch only works on the Last Missions: Keep your friends close mission, the very last mission.
Watch out there is a SPOILER ahead!

Some time into the mission you have to kill Lance on the roof of your mansion. After you killed him don't go back into the mansion to Sonny, but jump from the roof to normal ground. Blow up all the limos in front of your door. After they all are done grab the Infernus and drive to the western island. Now drive north or south, it doesn't really matter, but north works best. After some meters you map will disappear, this is interesting already. Now watch your surroundings while you speed along the road in a fast car. Everything becomes a blur and looks like you are drunk.

You absolutely need a Golf Caddy for this Glitch. You find a lot of them on the Leaf Links island, but most of them are in the fenced in area, but sometimes there are golfers driving around outside of Leaf Links. Also you can drive out of the golf course via the ramp to the west of the club house. Or you search for the Caddy in the bushes around the lighthouse in the southeast of the first island, there is one hidden there. Once you have a Golf Caddy drive it to the Northpoint Mall.
I like to save my Caddy in the garage of the El Swanko Casa just because the Glitch is so cool and I sometimes want to activate it just for fun.
So, drive your Caddy to the NPM.
Maybe you noticed you can't drive into the Northpoint Mall with a normal car as you don't get it through the narrow door. But you can drive a motorcycle into the NPM, the game loads and you are inside and can drive around in here. But with the Caddy you can make it through the first open door of the NPM. That's cool, isn't it?
No?, well then drive on, you can now drive through the black wall at the back of the entrance area as these walls are non blocking. That's cool, isn't it?
Now you are inside this rather strange looking Northpoint Mall. Get out of your Caddy and take a look around, explore the ghostly escalators and so on. Then try to leave the Northpoint Mall. Suddenly you are inside the normal NPM and your Caddy is also still in here. Well, do you have an idea what great thing you could do now?
Right, get in the Caddy and leave the same way you came in.
You enter a really cool and strange ghost world where people are hovering through the air, cars do so too and you can see all the weapons and icons.
Have fun running into invisible walls :)