I'm assuming that this is a pretty shady area, since it's between a fence and a house. I'm also assuming that it will get walked on occasionally for basic house maintenance, so tripping hazards are something to avoid. For myself, I prefer groundcovers that are relatively well-behaved and easy to kill should I change my mind. Here are some ideas for you for zone 4; they're in order of my own personal preference:
Mazus reptans - very nice, very low groundcover with pretty blue flowers in late spring. Establishes itself pretty quickly.
Carex pensylvanica - This is a sedge, so it looks like 5-6" tall grass clumps until it grows into a green shaggy carpet. Rhizomatous, so it spreads pretty well after the first year in the ground. A popular choice in Southern Wisconsin for many landscapers for exactly your situation.
Hosta - Not a traditional groundcover, but if you plant a row of hosta between the fence and the rock they will, in only a couple of years, completely shade the ground. An advantage to hosta is that you can probably find someone you know who wants to get rid of some - or, if your area is like mine, you might find a pile of plain old green ones on the side of the road for free. One possible issue (depends on how much you like your neighbor) - because the leaves are so high off of the ground there's a good chance that the hosta will trap moisture and help rot the fence.
Liriope splendens - A grassy groundcover. Liriope is much-used in the Southern US as a great filler plant, with nice flowers. Supposedly hardy to zone 4b.
Sweet Woodruff (Galium odoratum) - A pretty little thing that covers ground very fast. My sister gave me a two-inch diameter clump once, and three years later it took me 6 hours to get dig it all out. I estimate it spread about six feet in three growing seasons.
Lily-of-the-valley (Convallaria) - This will take over the area and probably grow into the rounded rocks, too, as soil filters between them. Note that this plant is considered an invasive species and restricted in some states. It's also very difficult to remove (usually done over two or more years).
Ostrich fern (Pteretis nodulosa) - This is quite tall and spreads by the ferny equivalent of rhizomes. It will, guaranteed, eventually leave the side of your house for front and/or back of your house. It's easy to mow, though, in that case. Note that it also may promote rot on the fence. Possible tripping hazard, too.
Any Lamium hybrid - This plant is fast-growing and has colorful leaves. It flowers in early summer, but has a tendency to run wild, like ajuga and ostrich fern.
Any of the Ajuga hybrids - Bugleweed is one of my least favorite plants because it usually covers your lawn as well as where it's supposed to cover. I've also found that it's a "loose" groundcover, leaving openings where weed seeds can germinate. If you don't deadhead it the hybrids, you may wind up with seedlings that do not look like the plants you planted; of course, this may not be a concern in your situation.
Pachysandra terminalis - Another much-running plant, difficult to eradicate. Nice flowers, though. Evergreen.
Note that I haven't checked any of these for toxicity to dogs or other animals. This should be a consideration for you, given your neighbor's dogs and that the groundcover will certainly go under the fence into their yard.
There are lots of other plants, like Epimediums (barrenwort), Mitchella (partridgeberry - a native plant), or Dicentra exima (fern-leaved bleeding heart) that make decent groundcovers, but they're expensive and don't grow particularly fast.
