Can bodyweight exercises work just as well as doing exercises with weights or on a weight machine?

I believe some of them do, especially those for upper body such as push ups , triceps dips, pull ups, or  all kind of planks. I think lower body needs more resistance for better or quicker results.

I agree! However those small muscles in the leg like the hip flexors can get a great workout with body weight-only movements as well as adding ankle weights. The larger leg muscles will need more resistance for the most part.

I definitely agree Mrsprincess, the larger leg muscles need more resistance. I use a stepper, the wave, ankle weight, body bar, and body weights to work my lower body. The best results I have gotten is from inclining my stepper and doing leg presses on the 14" setting, while using dumbbells.

I love using my step on an incline! I purchased the slanted risers and I love how that changes the feel of my leg workouts! 10-14 inches does wonders for the lower body, especially that region between your butt cheek and Hamstrings.

Definitely!

Some workouts specify that you can just use your body weight instead of hand weights.

I know a lot of Jari Love's workouts say this, not sure if they all do.

Well, I do OK but then I've got a WHOLE lot of body weight to move!  I look on the bright side.  I have some weights, but I could never afford all this weight, and I don't have to worry about putting it all away afterwards! 
On the other hand, if I ever got a tattoo like some people who hang around Gold's or somewhere might do, people might mistake me for one of the machines.

craig ballantyne created turbulance training which is an all bodyweight workout program.  None of the workouts use weights at all.  he is also a contributor to mens health mag.  there is a huge variety of exercises to do with body weight.  i do both.

Second the Turbulence training. If you can do a full chin-up or pushups,that, IMHO is real strength.

nmhemeon


craig ballantyne created turbulance training which is an all bodyweight workout program.  None of the workouts use weights at all.  he is also a contributor to mens health mag.  there is a huge variety of exercises to do with body weight.  i do both.

I agree, Craig even shows you how to use just body weight to train lower body, and so does
Zuzana of Bodyrock, both of these people have incredible, athletic bodys just from body weight exercises, and a good diet. Craig doesn't believe in cardio, per se, he does all of his body weight exercises in a fast circuit-like way which he says gives him his cardio, and lately Zuzana trains this way also and rarely uses weights. I been experiment just working out this way, it's tough, intense, fun, and effective. Also you can use a TRX
to make body weight workouts even more effective, this piece of exercise equipment solely use body weight, in fact their slogan is " Make Your Body Your Machine" I've been using Body weight exercises, TRX, and Kettlebells (love Kbells to much to give them up), and and for me they're just as effective If you're not living on the edge....than you're taking up too much space !"-Jay Johnson from Bootcamp Fitness