Since, hopefully, you do not wish to cause unnecessary pain to the people the deceased was in online contact with, make sure you know how the online service you are about to go into works - before you go into it. If you're not sure how this service or website works, ask for assistance from someone who does.
For instance, if you go into an e-mail account of someone who is no longer alive, and this e-mail service also has a chat or a messenger service, such as Gmail, Yahoo or Hotmail, the first thing you need to do is go offline. Otherwise, you might cause their friends heartache - or a heart attack - by seeing them seemingly online and available for chat.
Same word of caution about Facebook: if you choose to go into the profile of the deceased, the first thing you should do is make sure your chat status is offline.
If you start using a computer previously owned by the deceased, first thing to do is log out of every single web site they used to be active in, prior to your own use of the computer. If you don't, in a momentary lack of attention, you might enter a forum you're a member of, wishing to post a note under your own username, only to find out a minute too late that by mistake, you published under their username instead of yours - and caused that heartache - or heart attack - after all.