"Pain God" by Barclay Shaw
The simple answer is: of course!
There are two basic kinds of suffering: physical suffering and emotional suffering. Physical suffering occurs when things go wrong with the body and emotional suffering occurs when something happens which results in a emotionally painful pattern of thought.
Physical suffering is absolutely essential if we are to live in this reality with a physical body. Without pain sensors the body could not be kept safe from injury and could be maneuvered in ways which damage it. Pain is just a warning signal to tell us to stop what we are doing. Similarly with emotional pain- it is the emotional body's warning to us to stop thinking what we are thinking as it is damaging us on a mental and emotional level and also, ultimately, on a physical level.
To come to the end of suffering on an emotional level we need to practice what the Buddha taught which is detachment from events- the ability to feel equanimous no matter what happens. Any kind of agenda or attachment to outcomes will result in emotional suffering, sooner or later.
When it comes to physical pain this can be avoided in two main ways. One is to treat the body with care and act so that the probability of injury is minimised. Secondly, pain is avoided by not encouraging disease in the body by poor habits, including habits of mind. The physical body is the last warning system we have (after the emotions) to tell us that our thinking habits are poor. The existence of disease in the body generally suggests either a poor diet, a lack of appropriate exercise or a lack of attention to our emotional state. Uncomfortable emotions will eventually result in a sick body. This is avoided by focusing predominantly on thoughts which feel good emotionally as we think them. This will minimise, if not eliminate, pain causing conditions in the body.
I am not expecting people to be perfect and the idea that we should be living a pain-free existence may be actually a barrier to living a largely painless life by making us feel a failure for not doing so. However, it is important to realise for most of us that we have a great deal of control over how much suffering we actually experience in our own lives.
See also: Why doesn't God end our suffering?