The ground cover variety is invasive. The shrub form is not. I dug out all the ground cover I had, and last fall I put in a shrub form, and it is blooming well right now, with no spreading. In most plants there can be numerous varietals, that have totally different behaviors. (That can often be a real pain, in deciding what to plant or not. I take my Sunset National Gardening guide with me when I shop, so I can look stuff up, for the nitty gritty, before I buy it. It has its own zone system, which is better for marginal plants, also.)

Where do you live? (state, zone?) Is this a recent photo -i.e., are these growing now? I enlarged each picture a lot. Reading top row, L to R: 1, 2, could well be alyssum but the foliage does not seem quite right to me) but 6 definitely is alyssum (which actually IS an herb - Google it!). I agree with the consensus on #3; looks like grass but if you pluck some of the leaves & smells & tastes like an onion, it is chives. I believe #4 is a petunia (also may be considered an herb due to some ways petunias have been used; e.g., as a tisane- yuck - and the leaves as a pest repellent). Row 2, L to R: Number 5 is haunting me; I should know it, but I think it is something generally sold up where I live as an annual in a hanging basket (like a verbena). Number 7 is thyme; w/o being able to smell it cannot say which cultivar, but it looks like English/French/winter or whatever "ordinary" culinary thyme is, depending on what nursery sells it & what they name it. The last one certainly is a rosemary.

5 looks like a creeping Verbena to me, 7 looks like a silver or variegated thyme (thus the reason we need larger photos) and I agree that 6 looks like alyssum, 8 like rosemary, 3 like chive, and 4 petunia. One and two don't look like culinary herbs to me - perhaps purple and white alyssum? If you can post each of the original photos in its own followup to this post, you should get confirmation.

Aaah, I think that's it, jekeesl. The very toothy leaves resemble the plant pictured. (Wish I had the presence of mind to get a close-up of the leaves to help with ID, but I'm sure I was half heat-stroked already.) I'll pass this additional ID along to my neighbors. Thanks!