I work in a group home and was the only one using fresh parsley and it didn't ever last long. I started wraping it in a paper towel and then putting it in a plastic bag in the frig and it would be good to use the next two weeks.
You can also put it in a glass of water and put a plastic bag over the top, it will stay nice for quite a while - just need to change the water every couple of days.
My first post on this forum!! Just want to add to Jan's idea re the herbs, this is the way I keep my lettuce fresh longer also. I cut heads in quarters, wrap in p.towels and put in plastic bag - lasts a long time, don't know how long, 'cause we use it up.