How can I pass parameters to a block? Is it possible to programmatically pass parameters to a block?
Per the other answer, blocks are 'dumb' and don't have the ability to have arguments 'passed in'. They can, however, grab arguments from the context of the page, like node IDs, current user etc.

You have two 'easy' choices really:


Write your own block: It is pretty easy, if you can do a little PHP. Create a module and implement hook_block(). There are many examples on Drupal.org.
Use the Panels and/or the Views module: Panels allows you to create panes that can have all manner of variables and contexts passed in, BUT without a special theme the block will have to live in the content area, not a Drupal region; so it depends on your site, and where you want the block. Views can create blocks too, and receive arguments from the page URL, current user and also custom code via the Views PHP module. Views and Panels work together very well.