My deadnettles (three varieties) are very well behaved. They are not aggressive enough to keep down weeds, & they are not evergreen so winter-germinating weeds can invade. They seem to need a bit more care & very loose soil to look their best & wouldn't be my choice for difficult planting areas.
You want the evergreen perennials, commonly known as periwinkle, tha Paghat suggested - Vinca major and Vinca minor.
You could also try Pachysandra terminalis. It's gets bad press fo being a terminally boring plant but there's an attractive variegate one (Variegata, or 'Silver Edge') and it will even grow unde evergreens. It takes a year or so to settle down and start to spread.
At the risk of repeating what other people have already written, i might be worth including a few Lamium (deadnettle) for seasona variety, even if they're not evergreen in your area. Lamiu galeobdolon has leaves that are blotched with silver, and yello flowers. 'Herman's Pride' is a particularly attractive cultivar an better behaved. There are also plenty of Lamium maculatum cultivar with white or pink/purple flowers and beautiful variegation.
By the way, Wintergreen (Gaultheria), as mentioned by Paghat, is lovely plant, but only if you have completely lime-free soil. I mad the mistake of planting one in my previously rubble-filled garden an it died
Ours aren't completely evergreen, they seem to die back a bit in the winter. But a great deal of green/silver/whatever foilage remains. You must be in a colder climate or there is some other difference.
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