Marigolds.

zinnia and cosmos. Cosmos were almost 2 feet by the time they got outside!

snapdragons

sun flowers are pretty quick to grow

Marigolds come up quickly and I've had sweet alyssum come up the third day.
My plants had better come up quickly because I haven't been able to plant any since we're going to a softball tournament at Tulsa this weekend so am planting tomorrow and think I will take them with me in the car. Will have to lug them in and out of the motel and my sister's house, so if you hear a man screaming in southern Iowa Thursday morning you will know why.
Jeannine

OK, I didn't do them under grow lights but...my cannas from seed are 12" + in less than a month (including the time to germinate!)

Evening scented stock
(herb-chamomile I think it started to sprout up in 2 days or so)
Moonvine flowers grow really fast also

Nasturtiums

Morning Glories and Sunflowers became unmanagable very quickly when planted under lights. The morning Glories were tangled around everything they were near.
Don't know if they're going to be the fastest growing but The Statice I just planted Germinated in 1 day, Thyme and Dahlias took just 2 days.

Lavatera germinated in 3 days.....they are getting really tall. Melampodium, as I recall from last year, germinated and grew really fast. Love them both to pieces too.

~Deb

I started some monkey flower seeds (mimulus) back in February, probably about a month ago, and they've been under lights since they germinated. They started blooming yesterday. I had to make myself late for work because I was compelled to pinch all of the buds off so that they would branch out and bloom once I put them outside in a month or so!!
Also, I have black eyed susan vine (thunbergia) growing indoors under lights and theya are HUGE! I keep pinching them back as well.