Second one is Fleabane and the third resembles Ligularia

If the first has very small basil leaves it may be a boxwood basil. I just got one, and it has been pinched and is literally become very full like a small boxwood plant. I was told it does well indoors, so I'm hoping for winter basil this year. Mine smells just like basil but looks like a miniature basil.

I thought second was an ox-eye daisy, but I can't see the leaves or flowers well enough. Fleabane sounds like a good guess, too! Ox-eye is the wild daisy here, but I love them so I'm collecting them to put in the garden. Nice zen contrast to the traditional shasta daisy.

Don't know about the others, but I'll be interested to see the answers!

1 looks like it might be a globe basil, which has smaller leaves and as it grows will form a nice tidy ball-shaped plant. Doesn't produce a huge amount of basil, but very pretty in form.

2 reminds me of an annual fleabane that I got in a wildflower mix that turned out to be quite weedy, seeding everywhere. I'm still pulling volunteers many years later, as it seems that the seeds have a long life in the soil. Maybe Erigeron annuus?

3&4 The leaves look like Ligularia 'The Rocket' which has spikes of yellow flowers and likes consistently moist soil. See the fifth photo in this article:
http://www.finegardening.com/design/articles/gardening-in-damp-shade.aspx

photo 5/plant 4 reminds me of perfoliate bellflower AKA bellwort/Uvularia perfoliata, with the leaf veins going the length of the leaf and the stem sort of piercing the end of the leaf instead of having a separate leaf stem/petiole. (Uvularia grandiflora has similar perfoliate leaves.) However, the double top leaf (or is that just a trick of the photo angle?) and the lack of branching on the stem and the stem tip with those whispy bracts or whatever don't look right.

http://www.ct-botanical-society.org/galleries/uvulariaperf.html

Thanks for the help. I'll keep a watch on the basil - see how it grows. I didn't notice any discernible difference in taste when I tasted it. It may work nice when I want a basil garnish.

I think squirejohn is right with fleabane. When I googled it, I also see it grows in purple - and I noticed some purple ones blooming this morning. It's kinda pretty down by the pond, but I don't want it all over my gardens. I'll do some heavy weeding down there.

I also think my non-hollyhock is the Ligularia The Rocket. That would explain why the one in the shade is doing a lot better than the one in the sun. I'll move the sunny one into my shade garden and see how it performs.

nhbabs - that fine gardening link you provided is awesome. My shade garden is down by our stream, in an area that is pretty damp (and has been known to flood). I've bookmarked that page, which should help me add some variety down there. The only things thriving there so far are the dicentra and LOV.

Uvularia perfoliata doesn't look right. I'm not sure why the foliage turned brown. I'll keep an eye on the blossom.

I'm trying real hard this year not to pull anything out of the gardens until I know what it is. I'm trying hard to think about things as wild flowers, not weeds. Breathe deep and observe the foliage.

I'm pretty sure the third one is Telekia speciosa.