I was talking to my cousin about New Vegas, and we decided that followers should have special attacks.
First off, they can onky use them after a certain amount of time. For instance, maybe once an in-game day to use one. Also, you can control when they happen via the companion wheel. You could choose 5 options: (A) as soon as the attack is ready, (B) when there are 5 or more enemies, (C) against tougher enemies, (D) when companion's health is low, or (E) when player's health is low. They could also be turned off. Now for the attacks...
Rex: As he's a police dog, he would do the attack police dogs do where they jump up and bite down on a foe's arm. The target will be incapacitated until he gets Rex off, and the attacked arm is crippled. Also, friends of the target will be distracted by this, and may attempt to shoot Rex off of the target.
Boone: Boone could load a special clip of high-power incendiary bullets into his rifle, and would always hit with this attack. He might utter, "Here's the last thing you'll never see...".
Arcade: Arcade's was a bit tougher to think up. Based on his past, however, he would wield some type of overcharged prototype enclave weapon that shoots out extremely powerful and mildly explosive plasma bursts.
ED-E: ED-E would basically emit a loud noise, a sonic attack of some sorts. The enemies will be disabled for a few seconds.
Lily: (As I don't use her much, this may be irrelevant to a degree.) Lily could turn invisible, sneak behind the enemies, and sneak attack critical (one hit kill) several of them befor they notice her.
Veronica: I have two ideas, in case I catch flak for my first one. The one we thought up would be that she uses a signal of some sorts to call to Hidden Valley for air support. A Vertibird will make a pass, firing 1 rocket and a burst of the laser cannon at the enemies. If that sounds too crazy for you, then she goes into a berserk, punching every enemy in the face, crippling their heads, and afterwards disarming them.
Raul: Raul will live up to his Vaquero past, pulling out a second revolver and quick firing both from the hip (like a cowboy) until both have shot 6 shots.
Cass: As Cass has both an extensive knowledge of explosives and whiskey, this suits her nicely. Cass quickly makes a couple Whiskey fire bombs, throwing them at the enemies. They would explode over a bigger area and burn much longer than the actual fire bombs.
Lemme know what you think!