One big problem with wizards is that the higher level spells are more mana efficient. This means you'll want to use them, but they also cost the most mana. The result is that when you do something, it counts, but you can't keep that 'something' up.
Another problem is that your most mana efficient spells are AoE and groups prefer to take mobs one a one-by-one basis. The downside of AoE's are that they do not deal enough damage to kill mobs so you'll need more AoE'ers in your group to make it worth it. As said by Estu, this is hard to do at lower levels and requires specific groups.
The wizard IS good at nuking down a big target fast though. The wizard also has a wide variety of stuns at his disposal that can turn menacing casters/gaters into easy xp. The obvious problem with this is that they mostly happen at higher levels and with the former, you'll be out of mana afterwards.
Wizards thrive in guilds and raids. If you want to play an easy to level nuker, roll a mage. If you want to be a desired class, play an enchanter.
Also, try to group up till you're at least 12+.
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