When we're talking about large changes in evolution, for example giraffes growing long necks, we dont have any fossil evidence that supports the gradual adaptation model. We don't find fossils of giraffes with medium length necks. Not do we find fossils of worms with legs, or whatever. What we find are distinct species -- not evolutionary intermediates.
Well there are different ways of coming at this in my eyes.
I don't know what giraffes are supposed to have evolved from, whether it was camels or something, but lets say it was species X.
(1) So one X may have had a genetic copy error in one crucial gene, which spontaneously caused it to be born with a very long neck. Other X's may have shunned this child, but as it grew up it was better able to survive because of its ability to reach leaves on higher branches. Seeing this skill, it may have been considered a worthy mate by the opposite sex, and reproduction created more babies with long necks.
Now this long neck may have introduced complications, such as blood circulation problems, arthritis, inadequate neck muscles, swallowing difficulties. This is where gradual adaptation comes in, where the whole genetic code drifts from species X, to something better able to support the longer neck. This adapted genetic blueprint would be that of a giraffe.
(2) A birth defect, rather than a genetic error may have created a giraffe with a long neck. But still, this creature is better able to survive because of its ability to reach the leaves on higher branches. This child may carry its mother's predisposition to similar birth defects, and so the trait survives reproduction through a chain of female offspring.
The giraffe may not actually have a genetic code for a long neck, but a genetic code for a birth defect. And over time, there is this gradual adaptation, which 'refines' the uterus of the mother to perfect this birth defect, favouring a successful pregnancy and delivery of a child with it. There may also be a simultaneous genetic adaptation similar to (1) where the whole genetic code drifts from species X, to something better able to support the longer neck, and this adapted genetic blueprint would be a giraffe.
Furthermore, once the advantage is established, the genetics may then adapt to support long necked giraffes genetically instead of through a predispostion to birth defects. The birth defect trait slowly becomes redundant, as the giraffe becomes genetically defined with the long neck, although there is no outward sign of this change in the shape of the giraffe. So this stage could have taken a long time.
(3) Natural variation means that giraffes all have different neck lengths, and some are longer than others. We can hypothesise that the long neck evolvers were a minority group of giraffes -- a group with naturally slightly longer necks. There may have been greater sexual attraction between likenesses, so the longer necks are favoured mates by other longer necks. And this small group is highly inbread, causing their number to be kept to a very small percentage of the populus of species X, so no fossils. But as their neck length advantage grows, so does their survival rate, and gradual adaptation takes them to what we know as giraffes.
So to summarise:
(1) A random mutation creates a mutant with a significantly different feature, which is better able to survive and genetically adapts to better accomodate the mutation, so becoming the new species.
(2) Abnormal pregnancy conditions create a child with a significantly different feature, which is better able to survive, and it propogates through a maturnal line. These physical characteristics slowly become emulated via genetic adaptation, so becoming the new species.
(3) Gradual adaptation occurs within a small inbread minority group, which both drives them away from their ancestors, and focuses their adaptation. This group expands its population after it has better adapted, so becomming the new species.
Strange offspring happens often. Usually it is an impairment, whether that's from social exclusion or a physical or mental inability. But there's no reason why one can't get a lucky straw now and then, where strangeness is the beginning of something superior...
It also overlaps with
cryptozoology.
Other interesting related facts:
-- It is estimated that everyone has at least one genetic copy error in their lifetime. So when we die we're mutants.
-- There is the phenomenon of mosaicism, where a creature/person is a fusion of two different genetic codes. For example, your left hand side might be one code and your right hand side a different code. This may cause different coloured body hair on different areas of the body, or different eye colour, or different lengths of limbs. It can also happen with sex chromosones so that a person is genetically female upstairs and genetically male downstairs.
-- Plants can also have interesting genetic mutations, and when they do it can be spectacular. For example, trees can grow strange branches with weird leaves and creepy looking fruits. Imagine an apple tree with an anomolous twisty branch, bearing huge purple leaves and black leathery apples covered in long furry tentacles. Who would dare to eat it?
Theory by its very definition means that it isn't solid fact. Calling any statement blatant nonsense is an extremely close minded view.
Now all I need is for somebody to draw a picture of mean mr gray squirrel stealing a conker from a sad looking red squirrel. 
