Found here:

http://www.elderscrolls.com/morrowind/expansions/

I couldn't find this info on the forum here - my apologies if it has been answered.

While most of the expansions were hardly necessary (precursors to the "horse armor" that would come later), the "Master Index" quest was crucial to enjoyment of the game. "Siege at Firemoth" was interesting as well... but without that Index, the late game would be hopelessly bogged down with travel times.

If they don't come pre-packed with the game, will the downloads from Bethseda be compatible?

Thank you!

It has Tribunal and Bloodmoon.

It also has 8 optional plugins (need to switch on in launcher to activate), including Master Index and Firemoth.

There you go.

Thank you, and my apologies I forgot to mark this as a "question"!

I can confirm those official plugins are included, & also I have noticed that basically anything that worked with the retail version works with the GOG version

it's very cool to come to gog with a question and find a thread already exists that completely answers my question

rep all around

Yes, it's there, but it was officially released before Tribunal came out. With other words, the Master Index quest doesn't benefit from the upgraded journal. A minor inconvenience, but there is a plug-in fixing it, the Master index Journal Fix.
http://www.nexusmods.com/morrowind/mods/42482/?

Don't forget to activate the Master Index plug-in and the Journalfix!

The official plugins, even those on GOG, contain dirty references. I recommend cleaning them or getting an already cleaned version.

More on this on the official forums: http://forums.bethsoft.com/topic/1533488-morrowind-available-for-sale-on-gog/?p=24283180

As stated above bear in mind that the official plugins contain dirty references, most of them.
There is a mod made called Official Plugin Collection where those dirty references are cleaned.
It was uploaded earlier on planet elder scrolls, but since that site is gone you can find it at Morrowind Mod History.
Here it is: http://mw.modhistory.com/download-21-6169

I recommend using this instead: http://download.fliggerty.com/download--1079

It is based on the one linked by @candesco, but with improved cleaning and additional fixes.

Didn't knew they updated it. And by the way, Mw Mod history is also from fligg.

Is there a method to fix the problem manually by hand? If at all possible I want to avoid using a 3rd party program.

Also, if left in their default state what kind of problems should I expect to encounter when using the plugins?

The one that Ergos is referring to is just an archive containing replacement plug-in files. Extract the ones you want to use from the archive to the Data Files folder within the Morrowind installation and then from the game launcher select the new replacement plug-ins instead of the original ones. There is no 3rd party software fix involved here, just extract from archive and activate in game launcher.

To fix them yourself you would need 3rd party tools (e.g. TESTool, Tes3Cmd, TESPCD, but I'm new to Morrowind really so haven't used these and would rather not have to learn how to).

From what I understand, dirty references can result in different objects being referred to by the same name, so some descriptions may be wrong, some objects in the game may be wrong, some stats may go wrong, that kind of thing. Probably not much of an issue if you just use the Bethesda stuff, but still better to use clean references.

Don't use the default uncleaned plug-ins, simple as that.
I can't predit what will exactly happen but they will have an unintended influence on your game.
It was really unprofessional of Bethesda releasing them in their state.

If you want to fix the problem by hand you are going to have to use a 3rd party program.
Downloading already cleaned ones does not require a 3rd party program, only 3rd party mod files: I hope you are going to change your mind because you are going to miss out on a lot.
There are a lot of 3rd-party programs for Morrowind that a lot of people use and some are so important and good that they could be shipped with the game in the first place.
Similar to how Gothic 3 is sold with the community patches, Fallout is sold with the 1.2 patch and a high-res patch etc.

Mods ain't a third party program. They are modifications done by the community.
Also, most mods are just esp and esm files, not a whole program. Some mods are little programs, such as wrye mash. But if you don't want to use mods, well, then get used to errors and such, as Morrowind by default is not that stable.
If you left them in their current dirty state, then expect glitches or even a crash to desktop. It can become unplayable.
So i would highly recommend just to use the fixed plugins. They make the game more stable instead of lesser.
And also be sure to grab Morrowind Code Patch and Morrowind Patch Project as well. Those 2 mods are quite essential to use. Rest of the mods is completely optional. And if you ever use several kind of mods, then be sure to grab mash as well. Mash is the swiss knife to handle mods.

The plug-ins which are subject of this thread have been released by Bethesda, not by the community.