No, they don't. They do lose capacity over time, somewhat slowly, but it's not memory. Unless you're doing crazy stuff with unprotected cells, either the cell itself or its associated device (e.g. cell phone, iPod) will have a protection circuit and/or a smart charging circuit. LiOns are prone to explosion and fire if abused, so manufacturers can't cut costs by making the charger dumb.
BTW, memory in NiCd and NiMH is a myth. In typical layperson use, they will see capacity loss, but due to either overcharging (cheap dumb chargers) or deep discharging to cell reversal.