As has been repeated a thousand times above me, weighted chins and dips hands down. However, if you aren't strong enough to complete those movements properly, you could cause yourself some injury in the attempts.

Everyone seems to be forgetting the shoulders as well. Dips may hit the front delts a bit, but they won't hit them as directly as a targeted move. I think weighted chins hit the back delts a bit as well, but again not much.

If your not yet at weighted chins/dips(I have been working out consistently for 6 months and still have trouble with them thanks to bum shoulders I just now figured out how to fix): The EMG activity on a decently done pushup for triceps is actually pretty impressive. I would say if you can't hit 15 reps, solid straight back, arms scraping your sides, then do that for now. 3-4 sets, repeated maybe twice a day. (Aim for somewhere like 40-60 reps in a day, try to reach failure as this is the best indicator of muscle growth we currently have, in my opinion.) Go to your knees if you have to.

For biceps do barbell curls. Find a weight you can do for 6-10 reps, do 4 sets if this is all your going to do. (40-60 contractions, with muscle failure is a pretty decent muscle stimulus. Muscle failure is when you are going to lift the barbell and simply can't lift it anymore. Or you get stuck in a pushup.)

For shoulders, you have a few options, since a handstand pushup can be quite difficult. Build up to doing hand-stand pushups by getting into a pushup position and walk your butt into the air, maintaining a straight back. So your sort of an upside down V, and then widen your feet. Push straight towards your palms out in front of you, and then straight back along that same path. You should feel it in your shoulders and back.

Both the pushups and the reverse V pushup can be made harder by finding something off the ground to put your feet on, increasing the weight your triceps or shoulders have to work respectively.

Learning how do a good military press, side lateral raises, and bend-over lateral raises (or reverse dumbbell flies) will go a long way towards solid shoulder development. (Never neglect the bend-over lateral raises, failing to strength rear delts as many weight lifters do invites a slumped shoulder position and shoulder injury.) I would also recommend lying db external rotations 8-12 rep range. Don't push the weight too much here, but strong rotator cuffs can protect your shoulders.

Finally, once you have some shoulder stability and general strength to approach dips and chins, etc. incorporate negatives. So if you can't do a chin yet, jump above the bar and lower yourself down slowly (about 5 seconds down) Do as many sets of 2 as you can (stopping at 10), until you can do some actual chins. Then mix and match until for muscle fatigue. (Be careful with negatives, they freaking hurt, and can take awhile to heal from. Eccentric movements cause the most muscle tissue damage, but you can lift something like x1.8 more weight.)

Same thing for dips, but negative dips can be difficult to pull off properly without proper stability.

But honestly, if you want bigger arms, you gotta get bigger everything. Chest, back, legs, etc. can't be neglected for an aesthetic body. Let me know if you have any questions.

Check out nerdfitness for this beginner body weight routine and others: http://nerdfitness.com/blog/2009/12/09/beginner-body-weight-workout-burn-fat-build-muscle/

I'm against any of the traditional gym stuff like curls, pull downs, etc. Pull ups are good, ring dips, muscle ups - both bar and ring. But I made my largest gains rock climbing. I used to climb a lot but got out of it for a couple of years while I focused my energy into crossfit. Now I've dialed back the crossfit (a little) and added two days at the climbing gym and in just 4 months of that I've really filled out above and beyond what I got with crossfit.

I noticed that on typical crossfit work there's a lot that strains your shoulders in a bad way. Kipping pull ups, OHS, etc. But after a day if climbing all of that shoulder pain goes away. Even though climbing uses a lot of shoulders it seems to be in a way that helps them heal rather than beat them up.

Chins and handstands/hand-walking/HSPUs!

2 basic movements: chins (with palms facing you) and dips and consistent effort,

No hack required. Do work Son!

You want to get big muscles, lift big a$$ weights. Pretty simple.

Triceps work (close-gripped bench presses, french presses) add more size to arms than biceps work (curls) by virtue of the triceps being a larger muscle. Plus, in my (and many others experience) triceps can handle much more volume/frequency without fear of injury that biceps can.