As the deku leaf is one of the most useful items in the game, the only time where it would be skipped is in a Low% Speedrun. This is by far one of the hardest items to skip in the game. Skipping the deku leaf is primarily based upon using zombie hovering in the areas where the deku leaf would normally be used, which entails always making sure that your wallet is full of rupees so that you can purchase red tings, 20 rupees each, to heal yourself. This page shows how the Deku Leaf can be skipped in various important parts of the game where it is not trivial.
Obviously because you don't have the deku leaf, you cannot enter the Forbidden Woods in the traditional manner.
The first way to enter FW without the Deku Leaf is by using Door Cancel. With Door Cancel, it is possible to pop up from the water into the FW island wall collision. Then, by going very slightly ESS up on the control stick, it is possible to slowly climb the island all the way to the dungeon entrance.
Another way is to zombie hover over to the entrance and heal yourself with a red ting. If you have already obtained the Bombs Early, you can save yourself some rupees, if not, you can use a deku baba to damage yourself and start your hover. However, there is a high chance that if using the deku baba that your angle will be altered. Otherwise, you will have to purchase a Tingle bomb to start your hover, which costs 10 rupees each.
Finally, a TAS can also enter the Forbidden Woods with a Tingle Balloon Superswim from Outset.
The 2nd and 3rd rooms of the Forbidden Woods usually require the leaf to go through. It is possible to skip the requirement by zombie hovering and healing with the tuner, once again.
They can also both be done without zombie hovering, The second room can be cleared with chest storage and two tingle balloons. The third room can be cleared by using chest storage and precise jumps:
Since the Deku Leaf gives you the magic meter by default, you will not be able to obtain it before the Forbidden Woods. However, since items such as the fire and ice arrows require magic power, you will still need the magic in order to complete the game if you do not also skip the bow. To obtain the magic meter, sail to Two-Eye Reef (quadrant D7) after getting farore's pearl, and defeat the Big Octo for the double magic meter. You cannot sail in the Two-Eye Reef quadrant before beating the Forbidden Woods.
In order to skip Magic completely, not only you must perform every trick that Deku Leaf skip requires, but you must also skip the Fire and Ice Arrows as well as the Light Arrows. To skip the Fire and Ice Arrows and steal beat the Earth and Wind Temples, one must enter Fire Mountain and Ice Ring early without the Deku Leaf. Because you can not freeze moblins, you must also have Medli in the Earth Temple, meaning you cannot perform Hyrule 2 Skip.
To skip the Light Arrows without the Deku Leaf, you must either use Actor Unloading to unload the Phantom Ganon wall, or perform the trick shown below.
Because skipping Magic means you cannot shoot light arrows, you must also skip Puppet Ganon in a way that does not require magic, for example by dropping a bomb by landing on the ground with storage while zombie hovering (TAS-only).
Once again, you can get past all the deku leaf requirements using zombie hovering. It is interesting to note however that you can skip the deku leaf requirement in the first room by using a Tingle Balloon, or by using Spring Jump Storage.
To skip the leaf in the 2nd room without hovering, play the Command Melody to get control of Makar and fly above the gate to land on the other side. Then step on one of the switches to rotate the gate. This method only works on the US and PAL versions however, because these switches don't exist on the JP version. On the JP version, you must zombie hover over that rotating gate and heal with the Tingle Tuner.
In the main room, you can shoot the warp pot with a fire arrow. With the tingle tuner, you can also zombie hover to the warp pot. No matter the method you choose, this allows you to open the fan to the lower levels. You can then enter the miniboss early in a few ways (for example by using spring jump storage or by using a tingle balloon or by healing from a hover with the tuner in order to get on top of the miniboss door, then roll clipping through it). Once you have the hookshot, it is not too difficult to beat the rest of the dungeon without the Deku Leaf.
Trials Skip normally requires the deku leaf. There is however one single way to skip the trials without the deku leaf: by using Actor Unloading. The bow is generally used for this, but any Actor Unloading setup could work.
Although Fire and Earth trials are easily completable without the deku leaf, Forest and Wind are a different story. With the Tingle Tuner out of commission while you're inside Ganon's Tower, you will have to find another way to heal yourself out of a hover.
In the Wind Trial, there are pots near the end, and the very leftmost one has a heart inside of it. When you enter, align yourself to this pot with the telescope and begin your hover. When you get close, you'll need to hover low enough to make a bokoblin aware of you and follow you around. You need it to break the pot, hope that the heart lands in a spot below you, and drop down onto it. From here, just hookshot up and fight Molgera.
For the Forest trial, this one gets even trickier than Wind does. There are 2 pinecones at the end of the tunnel, and the one to the right conveniently has a heart drop. Align yourself to the pinecone. Start your very tedious hover until you get near the pinecone. Once you reach the pinecone, drop a bomb, get hit by a Peahat, and immediately continue your hover until you're above one of the heart drops. Drop onto it and fight Kalle Demos to your hearts content.
Note: Because beating the Trials without the Telescope triggers the File Item Transfer glitch, skipping the Deku Leaf by beating the Trials requires obtaining the Telescope. The hovers are usually considered TAS-only.