That rarely happens to me. Mainly because I answer more emails than send new ones, and I simply click "Reply" which automatically selects the correct recipient. But when I send out emails I usually double-check the recipient to make sure it's the correct one.
The dangers are quite obvious. It's like planning a birthday party for a friend and send the email to that friend. There goes the surprise. Now imagine if you were discussing some more important business involving money, credit card numbers, passwords and such...
Nowadays very few people write the full email address though. They usually select the emails from their buddy list, which is a bit safer. You just have to be careful, especially if you send important emails everyday.
This is taken too lightly by some internet users. Even workplaces where they have a closed intranet have seen employees suffer the consequences of accidentally sending a bad email about the boss to the boss! Sending sensitive information to the wrong address can be easily done especially if you are not a careful person.