Bildungsroman is a German term which refers to a specific class of novels. What is important in determining what is or is not a classical bildungsroman is the intent of the author. Was the author attempting to lead the reader into a path of personal enrichment? Do the trials and actions of the main character provide a moral or spiritual example of development? Most novels are about some sort of progression of a character -- whether toward virtue or not -- but in order for a novel to be a bildungsroman the author has to have the intent of setting a pattern for the reader to learn something important from.
Huckleberry Finn is certainly a bildungsroman. Though the novel can also be termed as satire (which many, although not all, bildungsromane are) there is an definite didactic element to the story. Twain attempts to instruct the reader in the inherent injustices of the American society of his time, and he does so by the moral and social maturing of Huck. Many of the main elements in this book are present in other bildungsromane. The journey of Huck and Jim especially, which takes up much of the book, is the means by which Huck learns much about himself and the plight of the African Americans under slavery.
Jane Eyre, while a very different book than Huckleberry Finn, is no less a bildungsroman. The novel contains the story of Jane's life from early childhood through her marriage in young adulthood, with examples of the apprenticeship, education inside and outside of school, perfect love, and, most especially, the existential crisis which leads Jane to a better understanding of her own identity. These are all elements of bildungsromane.
Wuthering Heights cannot, probably, be termed a bildungsroman. There are certainly elements of that type of novel in it, but the progression of the main character, Heathcliff, is from moral purity and a state of natural goodness to a state of depravity, vice, and cruelty. Heathcliff's treatment of those around him, after Cathy's death, is the exact opposite of what the character in a bildungsroman should be doing when faced with suffering. We watch the utter degradation of Heathcliff's character, and witness the escape of those under his control, ultimately, into a state of regained peace and security. Wuthering Heights can be thought of many ways, especially as a psychological thriller, or even a metaphysical novel -- but a bildungsroman, probably not. Heathcliff's decline is too self-willed, with too many chances for his own redemption, for him to be a hero of progression and ultimate moral triumph. In addition, Heathcliff doesn't ever search for the meaning of life. He had found it in his Cathy, who abandoned him and then died; once she was gone Heathcliff's only direction was down. While the effect of Wuthering Heights on the reader may be the same as a true bildungsroman (that is, the didactic goal of teaching the reader something about progression of a character into something more knowing and better) it is taught negatively: Heathcliff is an example of what should not happen to a young person who wants to progress into a fully moral being. While readers may be enriched by Heathcliff's struggles and fall, it is by being taught what to avoid, rather than what to do. It is also not at all clear that Emily Bronte intended anything instructional in her novel. This could be debated, of course, but the pattern and major elements of her novel do not fit within the classical definition of a bildungsroman.