For more on the weapons associated with each class of gladiator, see Weapons of the Roman Gladiators.
William Smith's Gladiatores
Gladiators entry from an 1875 dictionary of antiquities on Bill Thayer's Lacus Curtius site.
Andabatae wore helmets without eye holes.Cicero mentions these in his Letters to His Friends 7.10
Sed tu in re militari multo es cautior quam in advocationibus, qui neque in Oceano natare volueris, studiosissimus homo natandi, neque spectare essedarios, quem antea me andabata quidem defraudare poteramus.
Ad Fam VII.10
However, in military matters you are much more cautious than at the bar, seeing that you wouldn't take a swim in the ocean, fond of swimming as you are, and wouldn't take a look at the British charioteers, though in old time I could never cheat you even out of a blind-folded gladiator.
Translation by Evelyn Shuckburgh
Catervarii did not fight in pairs, but several together.
Equites fought on horseback.
EssedariiEssedarii fought from chariots like the Gauls and Britons.
HoplomachiHoplomachi were like the Samnites, but more heavily armed. They wore ocrea on both legs and mail or leather cuirasses.
Laqueatores used a (laqueus) noose to catch their adversaries.
In Book XVIII of his Etymologies, Isidore of Seville xviii.56 says this about them:
" 56. OF THE LAQVEARIIS.  Laqueariorum fleeing the fighting had been in the game, were hindered in the snare of the men had been thrown consecutosque they cast themselves down, having a boss of his shield LURE.
Meridiani fought in the middle of the day, after the wild beast fights. They were lightly armed.
Ordinarii were the regular gladiators who fought in pairs in the ordinary way.
ProvocatorProvocator was armed like the Samnite with a parma and a hasta, his opponent was often the Myrmillo.
Retiarius wore a subligaculum and a metal galerus on the left arm. He carried a net, a dagger and a trident or tunny-fish fascina.
In Book XVIII of his Etymologies, Isidore of Seville has this to say about the Retiarius:
54. OF THE Retiarii.  Retiarius armed troops from the genus. In the play against the other, a gladiatorial show, fighting valiantly, and bore it secretly, a net, that Like a club or named, as an adversary to cover the insistence by with his spear point, inplicitumque strength and surpassing him. What armed troops fought the cause of the forks to Neptune.
The Secutor carried a large oval or rectangular shield, an ocrea on his left leg, a round or high-visored helmet, manicae at the elbow and wrists, and a sword or dagger.
In Book XVIII of his Etymologies, Isidore of Seville has this to say about the Secutor:
55. OF THE SECVTORIBVS.  from the secutor is pursuing increased the Retiarius the said. For a cusp, and had seen him wear the weight of lead, which the adversaries to discourage Like a club or, as a net to strike the blow before he, this man shall exsuperaret. This was the armor of Vulcan, the sacred. A fire for it is always followed, and for that reason since the Retiarii, composed, for a fire and water is always to each other are harmful.
Thracians (Thraeces) carried a round shield and a short sword or dagger (sica, Suet. Cal. 30) or falx supina (Juvenal VIII.201). They wore visored helmets with wide brims and ocreae on both shins, according to Barbara McManus.