Social Media Headshots
Social media does not have the same formality as a corporate website. With the increased use of social media however, it makes sense to have images that convey a sense of professionalism, even if it's in a less formal manner.
Facebook/Twitter/Instagram Profile Image, Web Avatar, Personal Website Profile
Not everything needs to have a formal 'business' look but as a professional, nothing sells professionalism to clients more than having professional looking images that extend beyond your corporate or business site. The face you present in public is what you will be known by and an underexposed, duck lipped cell phone selfie is a surefire image killer.
Have fun while expressing your inner self
People want to know who they will be doing business with and sites like Facebook and Twitter are the principal places clients go to find out who they will be dealing with. The image you present on social media should receive the same care and attention you give to your professional brand. While that brand may be all business, your social media brand can reflect your playful side.