MichaelH

See what happens if you update your Permalinks via Administration > Settings > Permalinks

<?php
$cat_id = get_cat_ID('yourcategoryhere');
$args=array(
  'cat' => $cat_id,
  'post_type' => 'post',
  'post_status' => 'publish',
  'posts_per_page' => 3,
  'caller_get_posts'=> 1
);
$my_query = null;
$my_query = new WP_Query($args);
if( $my_query->have_posts() ) {
  while ($my_query->have_posts()) : $my_query->the_post(); ?>
    <p><a href="<?php the_permalink() ?>" rel="bookmark" title="Permanent Link to <?php the_title_attribute(); ?>"><?php the_title(); ?></a></p>
    <?php
  endwhile;
}
wp_reset_query();  // Restore global post data stomped by the_post().
?>

Related:
Stepping Into Template Tags
Stepping Into Templates
Template Hierarchy
Page Template

Just a guess, but maybe a plugin is causing the problem so try deactivating them all and see if that fixes.

http://wordpress.org/support/topic/pulling-posts-to-different-pages?replies=2

In Administration > Settings > Permalinks set Category base to projects.

Could put a simple loop in your Page Template. The Pages article has some examples. Essentially it is something like:

<?php
$args=array(
  'post_type' => 'post',
  'post_status' => 'publish',
  'posts_per_page' => 2,
  'caller_get_posts'=> 1
);
$my_query = null;
$my_query = new WP_Query($args);
if( $my_query->have_posts() ) {
  while ($my_query->have_posts()) : $my_query->the_post(); ?>
    <p><a href="<?php the_permalink() ?>" rel="bookmark" title="Permanent Link to <?php the_title_attribute(); ?>"><?php the_title(); ?></a></p>
    <?php
    the_content();
  endwhile;
}
wp_reset_query();  // Restore global post data stomped by the_post().
?>

Use a one of the Conditional Tags.

For example

if ( is_category() ){
}

or

if ( !is_category() ){
}

Might look at plugins such as wp-pagenavi or even a breadcrumb plugins to see if there is something you might use (or change)

http://wordpress.org/extend/plugins/wp-pagenavi/
http://www.google.com/search?q=wordpress+plugin+breadcrumbs