Jogging is a good one of course. But in terms of in your own home.. I tend to do 30-40 minutes of mixing a whole bag of different exercises up. Shadow boxing (or a punch bag if you have one) , press ups, crunches, dumb bell exercises, squats, burpees, etc etc.. if cardio is all you're worried about, you should just be looking to do anything that builds up a good sweat really.
For a 30 min workout:
Do a 5 minute warm up (jumping jacks, shadow box, jog, skip rope etc)
Then chose 5 of the calisthenic exercises, and do them for 1 min each = 5mins.
Take a 1 min break, and repeat up to 4 times.
It may be tough at first so you may only finish 3 sets in 30 mins because of a longer break.
If you try to do 50 of the above jumps (1 includes 1 jump+1duck+1jump) in one of your 2 mins, it makes you cry. a little. and vomit. a little. You dont need the bars. Just jump over a rock, or a pair of socks, and just make sure you duck really low. thats what really kills the legs.
ANyways, let me know if you have any other questions about working out in an empty room. Im a pro at it.
ONe last thing I forgot to mention. Its only gonna be as hard as you want it to be. In 2 mins, I try to complete 50 pushups (various kinds), for the sit ups I'll try to get to 75-100 per set, I'll include another tough leg one, or a combination like burpees etc.
Any kind of circuit training with little to no rest is good for cardio training at home.
Here are some good exercises to consider for a circuit home routine.
Push up variations, russian twists, leg raises, Jump squats, lunges, burpees, pull ups, bent over rows, planks
Do a variation of circuit training, and actual long distance jogging. Circuit training will build your athleticism and explosiveness, but you need the long distance stamina as well, they are both important.
Proper training is must before start cardio exercise at home because if you don't have enough knowledge of cardio movements then it can make a big injury in your bones. You can do some basic stretching exercise at home.