Battlefield 1942 always stands out to me as the one that popularized large scale online battles on big maps with vehicles. At the time it was revolutionary in online gaming.
Command & Conquer: Renegade came out around the same time as well, with similar features. I kinda wish that game had a sequel as well.
Another gameplay feature that comes to mind is the exclamation/question mark above NPC characters for quests. I remember it first from WarCraft 3, but I think it really kicked off with World of WarCraft to get adopted by many more games.
I don't remember being possible to spawn on teammates in BF1942, but definitely remember it as a first to select spawn points on map like Battlefield always did.
There were a few BF42 mods that, on certain maps with certain vehicles, allowed you to spawn in vehicles.
IIRC, Forgotten Hope had a number of para-assault maps that allowed players to spawn inside of the aircraft they would parachute out of.
I believe you could also do this in... I can't remember the name of it, but the Star Wars themed 42 mod (which the BattleFront series either largely copied or was directly inspired by), I think it had some spawn-in-able vehicles as well.
Also BF Vietnam, the official game, used a similar concept of having 'tunnel exits' that could be built/placed by Viet Cong engineers, which were placeable spawn points, and the US had the 'Tango' ... mobile river boat with a helipad thing... which was a mobile spawn point.
I am 99% sure it was BF2 that first introduced being able to spawn on a player, I don't think any of the mods for the earlier games pulled that off always had to be a vehicle or placeable static object.
I can't remember if that mod had squad spawns. But I definitely remember playing it a lot, that was an absolutely revolutionary mod with so much content, not to distract from other great BF1942 mods though. I believe the original DICE team originated from that mod team to create Battlefield 2 as well.
DICE hired a few of the DC devs to work on BF2, then promptly laid them all off about 6 months or so after release, and then the laid off devs and others who weren't hired made Kaos Studios, and made Frontlines: Fuel of War and Homefront, before being corporate acquisitioned into non existence.
I'm not sure I've ever had more fun with any game than I did with BF1942. It was just so much fun. There were games with smoother play and deeper mechanics and better graphics, but none were as fun. The dumb mechanics made it amazing, like being able to lie down on the wing of a plane and snipe people while your buddy flew, or dive bombing and parachuting out at 10ft above the ground to capture a point, or shooting the main cannon from a tank into a barracks that has 15 people spawned inside it, or piloting a goddamn aircraft carrier and running it aground to get to a spawn point safely. It was so stupid but so fun.