It's definitely not basil. What was the fragrance like? Spicy, sweet, fruity, grassy, reminiscent of anything else (other herbs, food dishes, etc.)?

Maybe some kind of Monarda (Bee Balm)?

Yes I think it is bee balm as well - looks like mine right now. Here's a blog that has a picture - scroll down to May 12th to see.

Here is a link that might be useful: a garden blog

I'd vote for bee balm as well. There are several varieties, all with shaggy flowers that bees and hummingbirds love. It should bloom in late June/early July.

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I checked the plant again -- it has kind of a citrusy smell. Thanks to all who commented.

Lemon balm is in the same family of minty herbs but the plant doesn't quite look the same. Of course, there are different cultivars of lemon balm. There is also a cultivar of bee balm that is lemon scented. Here's some info and pictures I found about it:

Here is a link that might be useful: lemon bee balm

If you get red flowers, like the picture above, I'd say it may be bergamot. Looks a lot like mine, but mine hasn't flowered yet or I'd post a pic.