I spun this out as an offhand comment on this question but it made me think about it.
When we first meet Harry in Storm Front his powers are quite weak for a wizard and as the series progresses he gradually but consistently improves, mostly between books but sometimes within the book.
It appears that Harry Dresden follows the class progression of a Dungeons and Dragons Wizard as he increases in power. The progression appears to be that he is level one in Sotrm Front and gains one level after each book. For instance his favourite 'Fuego' spell seems to be very similar in concept to a Burning hands spell (1st level) as opposed to a Fireball spell (3rd level spell which he could use as a 5th level Wizard).
Is there any instance in the books of Harry using a spell that would be beyond his level if we follow the D&D Wizard spell progression?
As we don't know which set of rules or rules variant Harry may be following please feel free to use any D20 source.
There are a number of official and unoffical rulebooks which allow for different ways to handle spellcasting but the core D&D rules allow a Wizard to memorise four different spells at 1st level. Most optional rules then allow those spells to be cast more flexibly via some sort of spellpoint system.
The feats system introduced in D&D 3 allows Wizards to approach their magic use more flexibly too. For instance Harry, if he was based on a Wizard, could have chosen a metamagic feat that increases his power output at a cost in effort/spellpoints.
I've been rereading Storm Front the last couple of days keeping my idea in mind. Harry really does use only a limited repertoire of spells, mostly his wind push and pull, a fire blast, the finding spell, and his shield. While they definitely don't fit with the descriptions of D&D spells they are kind of similar with a little stretch of imagination and due to his use of a 'gust of Wind' lookalike spell you could easily roll him up as a 3rd level D&D Wizard with the right set of optional rules.
There is at least one notable exception. When attacked by a toad demon Harry manages to call down a lightning bolt which is a third level spell and only available to 5th level Wizards. However he does it by channeling the lightning rather than producing it which is something pretty much outside of most D&D rulesets.
I gave the answer to Jeff because he provided the key point about the Gust of Wind spell but everyone gave good answers, so thanks to all.