Am I allowed to remove the "Powered by WordPress" link in the footer?
Yes WordPress is licensed using the GPL v2 license so you are "free" to do whatever you want to with it ("free" as in "free speech", not "free" as in "free beer!".)
Since you didn't specify a theme , I'll assume you are using the default theme, now TwentyEleven, or one that is similarly built.
In the theme's root directory, you will find the footer.php file. Look for the following html:
<div id="site-generator"> <?php do_action( 'twentyeleven_credits' ); ?> <a href="<?php echo esc_url( __( 'http://wordpress.org/', 'twentyeleven' ) ); ?>" title="<?php esc_attr_e( 'Semantic Personal Publishing Platform', 'twentyeleven' ); ?>" rel="generator"><?php printf( __( 'Proudly powered by %s', 'twentyeleven' ), 'WordPress' ); ?></a> </div>
Delete it, and save the file, or you can replace it with your own link like so:
<div id="footer-links"> <a href="<?php echo home_url( '/' ); ?>" title="<?php bloginfo( 'name' ); ?>" rel="home'><?php bloginfo( 'name' ); ?></a> </div><!-- #footer-links -->