superdoobydo: I played Academy when I was younger and it was awesome. I didn't realize there were so many other games in the franchise :O I will be sure to grab the other 2 games. Thank you for your suggestions :D

Alexrd: Yes, Academy is definitely my favourite (and most fun) of the two. But Jedi Outcast is worth it for the story and it sets up Jedi Academy.

dr.schliemann: I'd suggest [url=https://en.wikipedia.org/wiki/Freedom_Fighters_(video_game)] Freedom Fighters[/url], but it's nearly impossible to get a legal copy of the game.

tinyE: i snagged a disc copy of it on Amazon a few years ago.

ZyloxDragon: If you can find a copy of it, Drakkan Order of the Flame. Ground combat can sometimes be a little wonky, but you do get aerial combat on a dragon, similar to good old Descent.

Strijkbout: If I may recommend something newer I would certainly try M&B Warband, I put over 500 hours in it (original M&B + Warband combined).

From the time period, Tomb Raider 1+2+3. If you can forgive these games that they're early 3D games with tank controls they're a lot of fun, a great experience even.

Fade to Black, one of the earliest 3rd person games, generally considered not as good as Flashback (rightfully so), I still liked it because it had atmosphere.

Aurora Watching or Soldier Elite depending where you're from, a solid attempt to copy Metal Gear Solid :) and I have a weakpoint for games where you have to infiltrate secret bases in the arctic.

Lifthrasil: My favourites have already been mentioned. So I can only repeat the recommendation in order of preference:

Max Payne 1 & 2, especially the 2nd is awesome!
Jedi Knight: Jedi Academy
Mafia
Outcast
Overlord
All the Tomb Raiders
Bloodrayne 1 (2 is meh)

Or if you also include role playing games, then there is of course:
KOTOR 1 & 2 (especially the first is great)

Edit: also really awesome, but published later than your 'time of publication window':
The Witcher 2 & 3 (especially 3)

Hikage1983: Noone has mentioned Oni yet i see.

Unfortunately, your best bet would be tracking down a physical copy since it is not sold anywhere digitally (for shame too).

Wishlist entry:
https://www.gog.com/wishlist/games/oni

EDIT: Gave up on trying to post the wikipedia link, thanks forum software!

huppumies: Ever tried Outwars? Fits the bill I think, and it's an awesome game.

Spectre: GoG should have better menu options to search throw categories like this.

I will add to the list,

https://www.gog.com/game/soulbringer - more of a RPG but you run around from 3rd person

https://www.gog.com/game/legacy_of_kain_soul_reaver - hack and slash with a story.

https://www.gog.com/game/shogo_mobile_armor_division - Has robot sections that are 3rd but other parts are FPS.

https://www.gog.com/game/die_by_the_sword_expansion - The game looks better with proper graphics mods.

Arma games let you play in 3rd person if you want but the company that made them pulled their games away from GoG using the gamespy shutdown as a poor excuse then stuck them on Steam a while ago