Annuals
Each year I start basil and dill from seed. I usually buy a couple of parsley plants because I've never had a lot of luck growing them from seed--they always bolted really early.I grow the basil in my greenhouse since it does wonderfully well there no matter what kind of summer we have. The dill gets planted next to the cucumbers as both a companion and a fun little bit of frivolity. Instant pickles as it were!
Perennials
I planted chives from seed the first year we were here and the original 2 clumps are still going strong. I've divided them and given chunks to friends and neighbors too.
The next year I planted spearmint, apple mint and lemon balm in the same bed with the chives and all three of them are still going strong. I planted the mints with plastic edging sunk deep around them to keep them from taking over the world. The lemon balm has been divided twice because it got HUGE. I've learned to cut all three of these plants back right after they bloom so that the birds don't spread their seed all over the garden.
I planted horseradish in the same bed with the chives and the mints. I really did think I'd dig it up every year, really I did. But of course after we had cried our way through making our first batch of ground horseradish (take the experience of peeling really strong onions and multiply it by about 10), I wasn't as motivated as I had been. Now I just dig it to keep it from spreading too far into the mint and other plants in the bed. Its huge spear-shaped leaves provide a nice texture in the center of the bed.
This same bed also has feverfew, a lovely herb that is supposed to be good for headaches. I've never used it for that but I've kept it because I love it's little white daisies that make a wonderful filler in bouquets. The plants aren't very long lived but they self seed really nicely--in fact bit too nicely some years.
Early on, I planted lavender here and there in the garden and the plants are getting a bit elderly at this point. You really do need to prune lavender every year to keep it from falling over and losing its nice form. I didn't realize that and have gotten into a bit a fix because of it. I've managed to renovate one of the bushes but a second bush hasn't responded as well to heavy pruning.
The sage I planted 20 years ago is still fine though.
I also have winter savory and tarragon in the bed with the sage.
A couple of years ago I renovated an old burm in the garden and planted it with herbs. The center piece is my pampered rosemary bush that had been living in the pot and spending the winter each year in the greenhouse. It did fine the first few winters but it looks like it hasn't survived the repeated cold (sometimes with no snow to insulate it) that we had the winter of 2008-9.
Along with the rosemary this burm has regular thyme(thymus valgaris) and lemon thyme (thymus citriodus "Aurea"), golden sage (Salvia officinalis aurea'), tricolor sage (Salvia officinalis 'Tricolor'), elfin creeping thyme, parsley and Corsican mint. Yes, I really did plant parsley, sage, rosemary and thyme together (Simon and Garfunkel rule!).
The oregano I planted in the early years escaped and self seeded under the grape arbor and along the fence line so I don't bother growing it in a formal bed anymore. It's always there waiting for me if I need it.
There are two more herbs that I've kept simply because I like to look at them: Sweet Cecily which has nice big white umbels and Sweet Woodruff which makes a great ground cover in areas that get some irrigation.