Because I was curious about something, I made this graphic for myself so I could visualize it. This is the entire Elementalist toolbox, as it were. Realistically, a player might only stick to one weapon (since Elementalist has no weapon-swap, and for good reason), a preferred healing skill, a preferred elite, and a set of three or more preferred utility skills.
However, as I've seen from many solo runs, a really enthusiastic Elementalist will use almost all of these skills, by swapping weapons from inventory before many encounters, using many of the utilities, and even using different healing skills depending on what they're doing.
This doesn't even take into account Traits, which add additional effects and passive abilities, like on-dodge effects.
This also doesn't show Racials, or skills that have auto-chaining skills that follow up from the first, or double-tap skills that require a second press to do an activation of an entirely new skill.
As Proven pointed out, this also does not include the skills from summoned weapons.
In a vacuum, the Elementalist has a skill toolbox that contains:
60 weapon skills.
4 healing skills
3 elite
20 utility skills
Which makes for a total of 87 skills a player needs to understand if they want to really get into what their profession has to offer. Now realistically, even with from-inventory weapon swapping, average play will only use about half that, but that's still around 40 skills.
Just for contrast, the Warlock in World of Warlock has 54 skills, and will at most use half of them simply due to skill tree specialization.
I had wanted to go through the Elementalist skills and make a tally for how many pure damage skills there are, compared to ones that offer support (cripples, slows, etc), and ones that offer healing, but I found that the Elementalist is surprisingly colour-coded. Most fire skills are damage, most water are support/healing, most lightning are control, and most earth are self-buff or damage mitigation.
It looks daunting, and yet... I'm playing an Elementalist right now and it's pretty straightforward. I know there is a lot of criticism levied against Guild Wars 2's limited skill bar, but the limit and auto-skill assignment makes a profession much easier to digest for me personally.
In Guild Wars 1 you had this giant toolbox of skills, but you could only slot six, and not change them mid-mission or out in the field, so if you made a poor build you were screwed unless you went back to town, losing all your progress. If you looked up builds online, they all involved skills you had to trek to go capture, and while many enjoyed that, it made following suggestions from other players very difficult. "Oh, you're on that mission? Just use X build". Except you can't, because the area where you need to be to get two or three skills for that build, is past the mission you're stuck on. And so on.
In World of Warcraft, when I was at the peak of my raid game as a Shaman, I used perhaps 20 skills at most, with the rest hidden away. Many people liked to have every single skill on their UI all the time, "just in case", but it was so edge-case scenario that they'd need them, it was really a waste of UI space. Heck, I even installed a few mods in WoW that basically hid skills unless they were needed as a follow-up skill, since healing rotations in WoW by the time Cataclysm rolled around was really pure rotation, and knowing who to use the rotation on. I know people in my raid group used addons like Spellflash to literally tell them which spell to use when, and they did as good as most of the people who learned how to know which spell to use when, themselves.
It's funny how, in spite of having generally more skills than it's peers, GW2 still applies a "less is more" philosophy in how it presents those skills to the player. It can give the impression of the game being overly simplistic, however. But I think that really boils down to player attitude. If someone wants to play simply, they will. If someone wants to play in a complex manner, they can. I'm glad the game supports both styles, even if one may be "inefficient". But fun is always more important than efficiency.
Bonus: A video of a Guardian in PvP being a total jerk - made me laugh: http://youtu.be/FE9DDY8w1Hk