Is working out triceps is important or can one neglect this muscle?

" Triceps" means " three-headed muscle " whereas "biceps" means "two-headed muscle". Triceps provide more mass to the arms than biceps, provides more " spring " to the biceps workouts and supplements the growth of the biceps and the arms.
These are opposing pairs of muscles. You can do alternate sets for groups like this , like one set of lats with one set of chest and one set of biceps femoris (front thighs) with quadriceps (back thighs) and one set of biceps and with one set of triceps.
Try this :
Do one set of standing triceps curls and one set of barbell or dumbbell biceps curls alternatively for the entire three or five sets.
You will feel the differrence in pump.
Read "Encylopaedia of modern bodybuilding" by Arnold Schwarzenegger.
Regards,
S.Suresh,
Trichy.

to have a proper weight balance I think you need to work the front of the arm (biceps) and the back of the arms (triceps) equally. I guess you could neglect it but why would you want to have strong sculpted biceps and weak, flabby triceps?

Definately try to work this muscle.
If not, then it will definately start to sag with age and jiggle when you hold out your arms.
I know- ew.
Plus, muscles in general are pleasing to have.