Here is an example of a HIIT (High Intensity Interval Training) workout without any equipment (from Michelle Felzmann):
1. Cardio Drills – 30 secs all out, 30secs moderate intensity, repeat each drill twice
a. Power squats/step touch
b. Step and hop (one leg)/jog on spot
c. Power plie pulse/alternating lunges to the back
d. Knee tucks/alternating knee lift
2. Exercises – Supersets – repeated each superset twice
a. Squats/Plank with knee drops
b. Plie squats/Single leg deadlift
c. Front back lunge/Plank rotation
d. Walking pushups/mountain climbers
e. Alligator pushups/Plank with knee elbow touch
There are lots of awesome body weight exercises you can do and just follow the HIIT principles. There are some good explanations of the exercises on here and on some of the referenced pages. Real HIIT is very difficult to do but the beginner exerciser can have good results with implementing the modified form.
Other exercises you can do with no equipment include:
Side Shuffles, Jumping Jacks, Power Squats, Power Lunges, Burpees, Lateral Hops, Scissors, Skipping, Sprints, High Knee Jogs...
Just remember that not every exercise is suitable for every person.