The most global and overarching skills and qualities mentioned by career experts:

• Communication skills (oral and written)
• Teamwork/group/interpersonal skills
• Leadership skills
• Work-ethic traits, such as drive, stamina, effort, self-motivation, diligence, ambition, initiative, reliability, positive attitude toward work
• Logic, intelligence, proficiency in field of study

Thus, these five skill clusters can be considered the most important in your first post-college job, and some or all of them will be required in just about any job in your career and can be cited in your cover letters as transferable and applicable skills that you possess.