Do I have to sign a copyright transfer agreement to publish an article?
It depends of what you mean by “an alternative”. If you mean an alternative to publish your article, you can certainly find other journals that don’t require that you grant them exclusive rights. Generally, that would mean an open-acess journal using the Creative Commons Attribution License (CC BY). Prime examples are the major OA publishers: PLOS, BioMed Central, and Hindawi.

If you mean publishing in a particular journal that requires coypright transfer, the answer is that granting them exclusive publishing rights is a publication condition, so that you can’t avoid it.

So what you gain in signing is... to have your article published by that journal. What you loose is highly variable among publishers. Often, they (who are now the copyright owners by virtue of the agreement) allow you (the authors) to keep some “rights” (I prefer to speak of “permissions”). Some publishers are quite generous, others not at all; you must carefully read the copyright agreement to know exactly what you will be able to do with your article.

Note also that some publishers ask (or propose as an option) an exclusive license instead of copyright transfer. Sometimes, they describe it as an advantage for authors, who keep the copyright on their work. But the truth is that some of these licenses give the publishers about the same rights as a complete copyright transfer, so that copyright ownership becomes an almost empty concept. See, for instance, Wiley, offering both without any difference in the actual rights transferred. Again, one has to carefully read the publication agreement.

Finally, in theory, one can always suggest changes in a copyright agreement, for instance deleting part of the text or adding some. There is also the SPARC Author Addendum, that you can attach to the copyright agreement, asking the publisher that you want to keep non-commercial use rights. The publisher may then accept these changes (usually by not responding, and publishing the article anyway), or refuse them. From what I read, there are both success and failure stories in that regard.