Here is a sampling of classes you may find at your local large fitness facility or at boutique studios in your area.  There are new ones popping up all the time and fusion classes are everywhere.   

For those interested, I've offered my 2 cents on what I like and dislike and my observations over the years on members' responses.  I've managed 6 fitness clubs and studios, taught at more, and attended too many to count  :)

1. Barre:     A non-impact workout using a ballet bar to tone the entire body.  Weights are very light if used.  (A personal favorite)
2. Functional fitness:  This class is formulated to work on moves that are needed to perform tasks in life.  Moves are multi-joint. (Non-dancers and men love)
3. Circuit training:  Moving from one station to another in a quick fashion to get a whole body workout. (There is not much time for boredom with these workouts.  I prefer circuits that do not use a majority of machines.) 
4. Cross fit:  Structured workouts of the day (WOD) are completed in these "Box" gyms that have a strong community component.  (Super popular with twenty and thirty somethings though can be designed for an older clientele. If you love competition, this may be a great fit) 
5. HIIT:  High Intensity Interval training  workouts are designed to rev up your metabolism.  Short, intense bursts of exercise are interspersed with moderate exercise at a longer duration.  It's a great way to increase your fitness but can be very intense.  (I would get a doctor's approval first if have risk factors.)
6. Spinning:  The phenomena of exercise on a stationary bike set to music.  If the class is done well, the instructor is dynamic and entertaining.  SoulCycle is a cult that has spawned many copy cats.  (On my list is to try SoulCycle.  I can't grasp spending $35 for an exercise bike class.  I took spin classes 15-20 years ago and they were great for a good sweat.  It's very quadricep dominant and I prefer to use my whole body most of the time.)
7. Pilates:  Joseph Pilates was the creator of this exercise method that works to elongate muscles, strengthen the core, and enhance back health.  It's low impact and in my opinion, a great way to get back into exercise.  It can be done on machines or as a mat class. 
8. Gyrokinesis:  Not as popular as Pilates but similar in that it is low impact and uses specialized machines.  I love the way it uses the full range of motion in a joint.  Worth a try if you have a studio nearby.  Pricey though.  
9. Yoga:  An ancient form of exercise that has been Westernized to provide more fitness benefits.  It is wonderful for flexibility and relaxing the mind.  (Another class that I need to fit in more.  I think everyone over 40 should do some form of exercise that concentrates on elongation and flexibility on a regular basis.) 
10. Cardio dance:  Choreographed moves set to music in order to elevate the heart rate.  (This was very popular back when I started 35 years ago!  It can feel like going to a dance party if done well and next thing you know, you are super sweaty.)
11. Step:  Another throwback to the 90's, Step was an alternative to the high impact aerobic exercise that was available.  It utilizes a step about 8 to 10 inches in height.  Great for revving the heart rate but is quad dominant. (I have a step at home and will use it for cardio as part of my program.  I mix it up:  do a little dance, a little step, some plyometrics, all in my living room.  lol)
12. Tabata:  Another form of high intensity interval training, Tabata consists of eight rounds of ultra-high-intensity exercises in a specific 20-seconds-on, 10-seconds-off interval.   (It's becoming a bit too intense for me at this stage of my journey.  I think about the risk/reward ratio and would strongly advise having a doctor's approval before pushing yourself this hard.)  

13. Cardio/sculpt: As it sounds, you get a bit of cardio work and body toning. It's a nice overall workout.

14. Cardio on machines:  Classes have popped up that have you rowing, running on a treadmill or using an elliptical as a class.  You'll get some stretches and usually some abdominal work included.  

15. Plyometrics:  Simply put, plyometrics is jump training . It is great for sport training though can be hard on joints.  Landings should be soft and with bent knees   Be sure to have.proper footwear.  If new to exercise or with risk factors, I would get doctor's approval.