Twitter and LinkedIn have similar procedures to close accounts and are easier to do than Facebook. They seem to all require a URL to an obituary so you had better make sure one is posted or you may be out of luck.
What happens when friends want to keep a person's profile active, while family members want to shut it down because it is just too painful? It is a hard decision and there is no easy answer.
Elsewhere on the internet, most postings are beyond any one individual's control. If the deceased person belonged to a group, wrote an article, was credited with providing a photograph, or contributed to any outside organization, family may be out of luck getting that information removed.
Being in the midst of this right now, my gut feeling is just to let things stay as they are for a while. Rational decisions are not at the forefront when dealing with the death of a loved one. Don't make it any harder on yourself.