Gymless Strength Training

Pushups are an excellent way to work the triceps, chest, upper back, and some variations work the deltoids more than others.

One could do pushups suspended between two chairs, or two beds--hands on one bed or chair, feet on the other bed or chair. For an extra challenge, do them on your fingertips and/or or with books under your feet or hands. Also, one could do elevated-legs pushups. Prop your legs up on a bed or chair, with your hands on the ground, and do pushups from that position. This variation works the upper pectorals and the lower back and deltoids more than the triceps.
If those variations are too easy, you could always throw a bag of something on your back--then, the pushups would become a strength exercise as well as a stabilization exercise.

Maintaining leg-strength is also important. For this purpose, one-legged squats work very well. Simply hold out one leg in front of you, holding it there with your hands if need be, and squat down until your butt touches your heel, and then come back up. Most people cannot do these, and those that can often cannot do very many of them. If you are one of the rare few who can do more than 10 or so of these, it may be time to wear a backpack while you do them.

For the biceps and forearms, we have chinups. Caution: working these movements without actual gym equipment could be hazardous to your health or the health of the furniture or room you're working out in (if you're in a room.)

For these, you could hang from a door mantle, or the door itself, if you are absolutely sure that it will hold your weight. You don't need to break any doors or anything doing chinups or pushups--that might just be embarrassing. Alternatively, if there's a good thick tree around, you could perhaps do them from its branches.

For the core (lower back, abs, and most of the waist) there are dragonflags. This is the exercise made famous by Bruce Lee. If you know what a leg-lift is (that exercise where you lay down and lift your legs straight up into the air), then you probably can figure out how to do a dragonflag. Essentially, a dragonflag is a leglift, except instead of being on your back, you're on just the back of your shoulders or a very small portion of your upper back, and instead of lifting your legs, you're lifting your entire body. It's a very hard exercise that most people cannot do. It simultaneously works the rectus abdominus, transverse abdominus, and the lower back.

If you are one of the very few people that can do more than 10 or so, you could tie a backpack around your feet and perform them that way.

Hopefully, these four main movements will help you maintain or improve upon your levels of strength until you can find some form of equipment to work out with.