When is it appropriate to use 亲爱的?
Yes, "亲爱的" does indeed has a slightly different connotation to the English "Dear". It is not used as liberally in Chinese letters and emails. "亲爱的" expresses a closer relationship than "Dear" does. The following are situations where you may or may not use it:


When is it definitely OK:
you writing to your spouse
you writing to your lover
you writing to your parent(s)
you writing to your colleagues
an organization writing to its customers or patrons
an institution writing to its students
When should I use my own judgement as to whether its appropriate:
male writing to a male friend
male writing to a female friend
female writing to a male friend
male student writing to a female teacher (depending on relative age)
male apprentice writing to a female mentor (depending on relative age)
you writing to complete strangers
When is it definitely NOT OK:
male writing to a female acquaintance
male writing to a female colleague
job seeker writing to the human resource department of a company
anyone writing to higher authority


In business letters (公函), salutations (修饰词) such as "亲爱的" are seldom used as it is quite informal and personal. Instead, "尊敬的" may be used if the letter is addressed to a higher authority. However it is often dropped, sufficing with just a title to address the person:


  XXX先生
  
  XXX经理


For informal letters, "亲爱的" is appropriate if it is used to express closeness in a relationship. It could be written by an organisation. However, on a personal level, care has to be taken to avoid misunderstandings especially when the addressee is from the opposite sex.