Disclaimer: All directions are given for right-handedness. Flip directions for lefties.
I will start with a couple of my favorites:
The grenade:
This is a very easily learned shot that more people should try. While it does not go very far it has the benefit of being very, very predictable and with an overstable disc it will straight in front of you every time.
How to throw it:
To start, you put your thumb UNDER the disc rather than on the top. The pad of your thumb can either be oriented against the flight plate or against the inside of the rim of the disc. You then throw the disc similarly to a spike hyzer (disc oriented vertical toward the ground in your hand) but you aim straight at your target between 30' and 70ish feet in the air.
Pros:
Again, this is a very consistent shot. The wind will not have much of an effect on it and it is very easy to control the distance. I will sometimes use this shot if there is a green where I absolutely cannot go long. It is also very useful in the woods to get back to the fairway because the disc is essentially vertical during the whole flight and it can squeeze through tight gaps in the treetops.
Cons:
It is almost impossible to throw this shot over 250ish feet. The disc will sometimes also roll or bounce a few feet when it lands.
Other things to mess around with:
Try throwing a flippy disc for a grenade. It can pan out and finish to the right for a very unique flightpath. Try throwing as if you were throwing a high flat shot but again, with the disc upside down in your hand. You can get a bit of left-right motion before the disc spikes, similar to the turn of a tomahawk.
Thumber roller
This is a more difficult shot that can require some practice but it is great for tight right-turn doglegs and for getting out of trouble.
How:
To start throwing this shot you want to use a very overstable disc (firebird, xxx, xtreme, trident, predator, max, flick). You throw the shot like a thumber but with the top of the disc pointed over your left shoulder. You are trying to land the disc on a 60 degrees angle to the ground with the disc leaning to the left. You will want to aim about 20' to the left of your line in order to compensate for the disc's motion before it lands on the ground. You may have to experiment with bending over to your left a bit to fiddle with getting the disc to land. The disc will flip over onto the flight plate VERY quickly once it starts rolling, especially with a less stable disc. The key is really to land the disc as close to the 60 degree angle as possible.
Pros:
If you throw this shot correctly with an overstable disc you can get 300+ feet of distance. If you land the disc closer to vertical you can get an upside-down u-shaped shot with the disc finishing rolling back toward you almost. This can very crucial on certain holes or approach shots. This is also a very good shot to squeak out of a tight lie in the woods. Because you release the disc close to vertical you can hit a tight gap and then get a roll down the fairway. If you release the disc vertical and throw it higher you can get a tight cut roll to the right.
Cons:
This can be a difficult shot to learn. It is not very useful if the ground is bumpy/rocky/rooty. It really is essential to have a very overstable disc for this shot. This is a very touchy shot in that if the angle of the disc is wrong when it hits the ground it can end up very far from where you plan.
Other things to mess around with:
Try throwing midranges or putters for shorter shots. Try throwing where the disc is passing almost flat over your head during the throw before you release it. See if you can roll a disc out and around the back side of a tree or bush.
Have fun and let's hear your secret shots!