I have always used dumbells and body-weight excercises for muscular development / strength training.
Do not underestimate the role of calesthenic / plyometric type / bodyweight exercises - unless you are a bodybuilder or power lifter they will prove better than "real" weight training.
There is an old book (privatelly published) called Muscle Dynamics, which goes into some detail about such training, based around the HIT / MMF principles - very very good!
Alternate these types of exercises with a range of open and closed had chin-ups and you will develop much better and quicker than just dumbells alone.
Here are some links:
Plyometrics
Calesthenics
My own "weights" routine consists of the following:
Wide Grip Closed Palm Chin-Ups
Narrow Grip Open Palm Chin-Ups
(these I do in a pyramid set style - 1st set 1 rep / 2nd set 2 reps / 3rd set 3 reps / 4th set 4 reps etc up to my Max (between 15-20) back down one at a time to 1 rep)
Calesthenic push-ups - wide hands
Calesthenic tricep push-offs - narrow hands (like a press-up but with my feet on a box so my body is paralel to the floor, and my hands flat (palm open) on the floor) I push up with my hands, pushing my hands off the floor - if that makes sence?
Hand Stand press-ups against a wall - take your trainers off so you dont have rubber marks on the wall!
Calesthenic ab crunches and ab cycling
I also on occasion use plyometric jumps with a ball, or weight, as I might duck walks with weight (dumbells)
Although I have and do use weights (dumbells); its all too easy to just "go through the motions" in using them. A good chin-up bar and body weight exercises gives you no choice other than to do them properly - as any gymnast would testify!
edited to add - try not to fixate on a specific number of reps (repetitions); instead, work to MMF (maximum muscle failiure / fatigue) this will ensure that you are pushing your ability to the edge each time!