Don't forget a certain tree in that great forest in the second world, one in which a major event happens. (I don't remember what that tree is called.)

Also, the Mana tree from Final Fantasy Adventure and the one from Secret of Mana. (Does such a tree appear in the rest of that series?)

The setting of Faxanadu is the World Tree.

Guardian Tree

The Tree of Mana is a mainstay in the series.

Yggdrasil in many many MANY games. We'll just put God of War (2018) here.

First one that came to mind: Entrance to Underworld 1 in Legend of Zelda.

Not a specific tree, but a dryad's tree from (insert any fRPG here).
Example: https://www.aonprd.com/MonsterDisplay.aspx?ItemName=Dryad

Treebeard (Lord of the Rings).

Guardian Tree (FF5).

On Dragon Quest: I most like how the tree was done in Dragon Quest Builders 2.

The Silver Sapling (well... not yet a tree in the sense) in Ultima Underworld.

Gildergreen in Whiterun.

Grand Oak Acorn that talks to you in Dragon Age. That's a nice tree:)

Path of Exile says hello

May I perhaps add one (in-)famous tree from a movie?
In case of a "yes": the Pink Bunkadoo in Time Bandits.

Randall:
"We made trees and shrubs. We helped make all this."

Kevin:
"Whew! That's not bad."

Randall:
"Yeah. But did we get a thimble full of credit for it? No! All we got was the sack. Just for creating the Pink Bunkadoo."

Kevin:
"Pink Bunkadoo?"

Randall:
"Yeah. Beautiful tree that was. Og designed it. 600 feet high, bright red, and smelled terrible."

Final Fantasy 3 has a dungeon that's a tree.

The original Dragon Quest Monsters, IIRC, uses a tree as the main town area.

The Elder Scrolls universe has quite a few of them. For example:

-In Skyrim is the Gildergreen and Eldergleam
-Black Marsh has the Hist, which are all over the place there and are venerated by the [s]master race[/s] resident Argonians (you can see some of them in Elder Scrolls Online); one Hist tree also appeared in Oblivion
-Valenwood has Elden Root (also in Elder Scrolls Online) in the center of its eponymous city, and the Bosmer love them some trees in general


There is also, as was hinted at earlier in this thread, the talking tree from Fallout 3.

SaGa 2 has tree monsters in it, and I believe the SaGa 3 remake does as well.

Now, these are just normal monsters, so not that significant, though it is possible to get such monsters in your party (your monster just needs to eat the right meat). With that said, in SaGa 2, the most powerful tree monster has a unique healing ability (heals the whole party and is stronger than a Heal Staff, but only 3 uses between rests).

Edit: Another one: Banjo-Kazooie's final regular stage, Click Clock Wood, features a giant tree that you can climb. You can even visit this tree in all four seasons. (The seasons gimmick is specific to this stage; other stages in the game don't have it.)

Somehow overlooked this earlier. YMMD
XD

Tech trees in Civilization and Age of Empires series.