It depends on what you are engineering! I think that when you mess with nature, you might get more than you bargained for. Seriously, you cannot really understand how the little things you do to tweak the tomato might actually affect it.
In some ways, I view genetic engineering as a modern component of "survival of the fittest" with a human influence. In agriculture, farming, and food production, for example, we genetically modify products to grow bigger, faster, and with less maintenence. We are in a similar scientific persuit to find new cures/prevention of disease and human suffering. The biggest pros of GE have potentially not been discovered yet, but if exploration in this area leads us to something great, it will be fully celebrated.
There are those who view this as "playing God" and refuse to support it. A couple hundred years ago, however, there could have been a similar thought about vaccinations. The cons, like any new scientific exploration, lie most in the unknown long-term results. In 100 years, will humans look back and wonder why things didn't get moving in this direction sooner? Or will they shudder at what has been created and wish their ancestors had just left everything alone?
If we're talking about agriculture here, the benefits are enormous. For example, scientists can create plants that need much less in the way of pesticides and fertilizers applied to them. This reduces the need for agricultural chemical use. It can also lead to higher yields, meaning that farmers can grow more food at a lower price.
The problems are mostly speculative -- they are things that might happen. People worry, for example, that genetically modified plants will cross-breed with unmodified plants, leading to unforeseen circumstances.
This is a huge question, as genetic engineering can be used in so many organisms and in many different ways, so I'll try to give you some general scope and a few examples.
In agricultural matters, genetic engineering picks up where selective breeding leaves off. Scientists have genetically engineered several important crop species to kill insects that try to eat them (Ex. B-T corn). The pro here is obviously fewer chemicals are required to produce our food. The con is that these plants may also kill beneficial or harmless insects, and that the genes that confer the pest resistance may escape through hybridization with other plants nearby. There are also those who believe that the B-T (for Bacillus thuringensis, the donor of the anti-pest gene) mechanism may damage the intestines of humans or farm animals who consume the plants.
Engineered animals are becoming increasingly common. Medical labs can now produce genetically engineered mice, called knock-out mice, where a specific gene has been deleted. This allows study of the gene's function. It's been a boost to researchers and a bane to animal rights workers.
In the human side of things you will find a lot of emotional content. Genetic engineering has the promise to provide cures to numerous maladies someday; diabetes and paralysis due to spinal injury are in the forefront of this research. This particular technology hasn't been considered too risky, as it will help with conditions that are already severely impacting the patient's quality of life. Genetic engineering of babies, however, is also being studied. These so-called "designer babies" have raised a lot of ire. Many ideas have been brought forth, from allowing parents to adjust their child's height, to controlling what talents the child is born with. At this point there are too many unknowns and physical risks to allow this to occur, but in the future it may be available; there is much debate about where the line is between improving life and playing God. The link below from MIT has a good ethical discussion about this.