Can I share my papers openly after publication?

The degree to and the format in which you can (legally) share your papers openly, for example by uploading pdf files to your personal homepage or any public repository, depends on your agreement with the publisher.

The Sherpa/Romeo database catalogues policies by journal for many publishers.

If a publisher asks for a transfer of copyrights during the publication process, you may be able to negotiate a more favorable agreement. The SPARC Author Addendum provides a template that (among other things) allows the author to disseminate a typeset version of the article for non-commercial purposes.