If your group plans on facing any heroic ^^ or tougher mobs, you will definately need a healer.
Here's the basic class breakdown:
Fighter: tank with low DPS
Scout: medium armor with high DPS
Mage: weak armor with highest DPS
Priest: healer
Within each of these classes are archtypes that add variations to abilities. For example, in the Scout class, one could become a Ranger (high DPS with a bow) or a Troubador (musical self and party buffs).
I've seen many announcements like, "Group needs tank!", or, "Group has 2 spots left, DPS prefered!" And the ever popular, "Group needs healer!"
Any class can be in high demand, depending on how a group is put together, but healers are normally in highest demand. Keep in mind that there is usually only 1 healer needed per group, so if there are many healers on, you may not be needed.
Good news is that there is a ton of solo mobs to hunt. :)