Stalkers are a reptilian-like species of animal that are able to cloak themselves due to a special organ they contain in their bodies. This ability to cloak themselves is powered by their shields and if they don't have any shield left, than they can't do it. Using this information, one can deduce that shock damage is extremely effective against Stalkers, but you need to keep the pressure on them so their shield doesn't replenish.
Needle Stalkers are the ranged type in their species, opting to stay back and shoot needles at you from their tail. If needed, they do attack in melee range, but it's a last resort. On TVHM, the needles they shoot at you deal explosive damage. There is a variant of these covered in slag (Slagged Stalkers).
Spring Stalkers like to jump in and out of melee range, pouncing on you or hitting you with their claws. They do not have any long-ranged attacks, so you don't have to worry about sneak attacks from afar.
As their name suggests, Ambush Stalkers like to remain hidden as long as possible, only coming out to attack their foes with a melee attack.
One of the more dangerous Stalkers, Cyclone ones can spin around while moving, dealing a lot of damage and even deflecting bullets. They can also shoot spinning spikes at you, making them even more dangerous.
Appearing rarely in TVHM, Rabid Stalkers will forgo cloaking themselves to get up and personal to continually bite the player. They appear more often in UVHM and give more experience than normal Stalkers.