We have had that exact problem this year around our deck. We decided that we'd rather have grass than anything, so we got grass seed for high traffic areas and we've been letting it grow in really well. I guess all the rain is doing it good because it looks great. Hopefully it will work. Other than that, I considered moss, mulch, stones, didn't like any of those options so we settled on grass. Good luck!

Depending on where you are in Oregon, you might try some other alternative ground covers. In milder climates, and in areas with light traffic, you might try Blue Star Creeper (Isotoma fluviatilis, also known as Pratia pedunculata or Laurentia fluviatilis).

I have a half-shaded concrete patio that used to have strips of wood between the concrete slabs. The wood rotted out and I replaced it with Isotoma. Now I have tiny little blue flowers between the concrete. It really makes the patio look a lot more inviting.

In shady areas, there's Irish or Scotch moss (Sagina subulata). You could also grow baby's tears (Soleirolia soleirolii, also known as Helxine soleirolii). I've also heard of people using one of the creeping mints, like creeping Thyme or creeping Basil in areas with light traffic and sun. These creeping varieties have very tiny leaves. When they get walked on, they release their wonderful fragrance.

The best thing to do is go to Google and do a search on the phrase, "lawn alternative". You'll find lots and lots of information.

Go to stepables.com. Lots of foot traffic groundcovers available. I have heretofore only seen their catalogue and website for mail order, but this season, here in NH, many of the nurseries are carrying their line.

We just ripped the grass out of two of our hell strips and planted wooly Thymus (12 inch centers).
It takes some foot traffic. Thymus 'Reiter' takes a little more. These grow together and form a low mat and are xeric. Wooly Thymus also can tolerate shade as well as full sun. I have stepped on the newly planted Thymus..the Reiter and a 'Pink Chintz' and they tolerated it and are now growing little extensions and sitting a little taller amoung the flagstones. The 'Reiter'blooms summer-lavendar and 'Pink Chintz' blooms pink.

I love though Veronica linwanis (spelling is not my gift). It blooms a beautiful blue early to late Spring and is a very nice green. It though does not tolerate the foot traffic as well. This one is so great when you have a tall flax in bloom at the same time...same blue!
Have fun! There are some great ground covers out there!

Istanbuljoy- I had not heard that wooly thyme could take shade - YEAH! I thought I was locked into scotch moss for those areas that I can't mow between the stepping stones. Stepables is a great site and you can probably find the same plants at your local nursery once you decide which will work best for you.