Adductor Longus
There are a bunch of hip adductors as you can see from the diagram, but why? If you ask most gym goers they're not going to say they're training "inner thighs" today. No one thinks that unless they naively believe that training a body part will somehow make it "skinnier." Like feeling the burn in one area of your body is going to burn that local subcutaneous fat. Tell me you don't believe that. Muscles get energy from local stores in the muscle and from the blood stream, not nearby fat stores. Those fat stores are just where your genes tell your body to place excess calories and activating a nearby muscle isn't going to somehow "melt" that fat. Please don't train the adductors searching for that elusive thigh gap (that's also more about bone structure and genetics than anything else).
So we have a adductor magnus and minimus as well as today's muscle, adductor longus, that also has a partner, the adductor brevis. If there is a big (magnus) there is usually a small (minimus), as well as a long and a short.
Of course all these adductor muscles adduct the thigh (bring it midline). Not really a super important action in everyday life, and as pointed out, not an action we do at the gym often with most of our movements being hip and knee flexion/extionsion during squats and deadlifts. Not that the adductors don't play a role in these movements. We have already seen the adductor magnus play a role in hip extension at the extremes of movement, and just recently I have felt some significant muscle soreness in the adductor area of my thighs after high rep deep back squats. Seems like I have some work to do with my adductor strength.
When the leg is not planted on the ground, adduction means bringing the thighs together. Not a very useful move although you certainly wouldn't have the agility to play any change of direction sport without adduction. Imagine trying to move laterally and ending up in a split. Not good. Side to side movement depend on the adductor group, of course. Therefore, the best training in my mind, is practicing those movements, defensive slid/shuffle. Forget the silly machines and awkward movements in the gym. Work on lateral movements on the field or court to build these muscles.
The adductors are also very active with hip flexion and extension stabilizing the joints, especially under heavy loads through full range of motion. The adductors pull the ball of the femur into the socket of the femur stabilizing the joint. To take it up a notch, go with one-legged (or is it one-leg?) squats and deadlifts. This requires even more stabilization around the pelvis to shift all weight to one leg and go through hip flexion then extension. Without strong adductors your knees will be wobbling through your pistol squat.
That's it. I don't have any specific exercises for this group. Just do your sport specific training and try to incorporate single leg exercises into your routine. In general, mimicking actual human movement in your training beats any shameful machine at the gym.