It can in certain cases be seen as heroic - for example, the soldier fearlessly charging into battle, with no care for his own safety, has a revered status amongst some. However, recklessness is more commonly regarded as a vice - this same soldier may be a liability to his own side, or get himself killed for no benefit. Furthermore, recklessness can also be a disregard for the safety of others, such as "reckless driving", and this type of recklessness is almost universally condemned.
Recklessness should not be confused with bravery. Although the two are related, the latter word is usually applied to cases where a person displays a more reasonable level of fear, rather than none at all.
See also: negligence