It is possible to keep a reasonable level of strength and conditioning without gym equipment? Absolutely. It’s not easy, though: extremely strong and jacked circus artists and dancers train for many hours every day. If the goal is to keep a reasonable level of strength and conditioning, then it is possible to accomplish that with bodyweight exercises only.
I strongly recommend everyone to have one or a couple of kettlebells and a set of bands at home. With that and a little discipline, you can keep training even in small places, like an area in your home where nothing will be knocked down or broken while you exercise.
There are infinite combinations of exercises with whatever movement split you adopt. Below are some links to resources. They can be used with a focus on strength, in which case isometric holds at peak concentric action and slow eccentrics are effective, or conditioning, using high volume, short rest intense training.
Example:
Day 1
Lunges – 5 X 10 (each leg position)
Single leg squat (not pistol) – 4 X 10
Two-arm KB swing - 2 X 20
One-arm overhead kettlebell squat – 3 X 10 (each arm)
Good-mornings holding a KB behind your head – 3 X 15
Band pull apart – 2 X 20
Crunches X hip raises – 3 X 20 each
Day 2
Pushups – 3 X 20
Dips – 3 X 15
Band side raises X front raises – 3 X 15 (each)
KB presses – 4 X 8-15 (depending on the KB weight)
Band assisted triceps extensions – 3 X 15 (each side)
Bicycle abs (obliques) – 3 X 30
Day 3
KB Single leg RDL – 8 X 5 alternating the leg
Vertical jump – 8 X 3
Side-walk with bands around your ankles – 3 laps (15 ft)
Band-assisted Nordic Curls – 3 X 15
Band-assisted biceps curls – 3 X 8-20 (depends on the tension of your band)
Crunches X hip raises – 3 X 20 each
Day 4
Pistol squats – 5 X 10 (each leg)
KB bent rows holding the concentric peak for 3 seconds – 3 X 10
KB clean & press – 8 X 3 (each side or both, if you have a pair of KB)
One arm KB swings – 3 X 20 (each side)
KB skull crushers – 3 X 15
Bicycle abs (obliques) – 3 X 30
More examples, demonstrations and readings:
The Bodyweight Warrior Program
Bodyweight Strength Training Anatomy