I don't want to pay to become strong.
So, can I become strong without going to a gym for weight training? Without equipment?
Really, the only equipment you need to gain strength is some floor space and something to hang on. And even the "something to hang on" is, in some people's opinion, optional.
If you can't afford, or don't want to, spend the money on typical gym equipment, then look into the various bodyweight exercises and plans. Convict Conditioning, Never Gymless, You Are Your Own Gym, and Yoga are but some of the things you can do to build strength with nothing but bodyweight.
Berin Loritsch says that you will eventually get to a place where bodyweight alone is insufficient. While he may be technically right, there's a catch - that point comes when you could (if you were doing so) do things like deadlift 2x your bodyweight or more. At which point, you've exhausted such things as muscle-ups, handstand pushups, jumping pistol squats, planches, shrimp squats, l-sits, and back bridges.
I, personally, prefer Yoga, in part because it naturally incorporates things like handstands and planks, so I'm not constantly doing mindless repetitions of things, but rather flowing through things and doing isometrics. About.com has an awesome Yoga section.
Oh, and if you think Yoga is only for women or isn't challenging enough to be of use, I challenge you to try such poses as Firefly or King Cobra, or this advanced version of downward-facing dog (and point out that plank, forearm plank, side plank, and several head and handstands come from Yoga).
There is always a price to becoming stronger. It's a question of how badly do you want to be strong, and what kind of price you are willing to pay. The biggest price you pay has nothing to do with money. The basic principles to getting stronger are:
You can do that in several ways. The quickest and most direct way is to use weights for resistance. This involves barbells, dumbbells, kettlebells, rocks, or anything that weighs a lot--including people. Since you don't want to pay gym fees or buy equipment, you will be using either body weight or unconventional weights for most of your exercises.
Another avenue is to increase resistance. While weights are a direct way to increase resistance, there is also isometric exercises and pushing against something that pushes back--like gravity.
The key here is to find something you can increase in difficulty. For example, if you are doing body weight dips and pull ups, you might look in to developing the strength to do muscle ups (starting with a pull up and transitioning to a dip all in the same movement). Then do it strict, and then slow. You might find some inspiration from Strongman activities as well.
Eventually, you will get to a place where body weight alone is not sufficient. You'll have to break down and start collecting heavy things to lift. This usually involves money, but hopefully by that time you will have an income that will pay your bills and have enough left over to buy the heavy things.
Someone posted a link to a Dragon Door article on bodybuilding a while ago to a similar question.
From the article:
I have been working through this progression for about a month, and while I am still on the first step of the progression, I have already noticed that my core and upper body are quite a bit stronger and am noticing more definition in my arms and chest. I imagine that lower body strength will follow once I move to the next step and my legs are no longer resting on my arms.
These exercises are free:
Paying money to a fitness center just means you prefer a clean and convenient way to do it.