The "No Subject" warning message is a feature new to Outlook as of Outlook 2010. It was a frequently requested feature in previous versions. When you compose a message and click Send without first filling in the subject field, the following dialog will come up, confirming that you want to send the message with a blank subject field.
Outlook 2010 / 2013 does not currently offer an option to disable this prompt. It is possible to use VBA to disable it (see Links below) however I don't recommend it.
To add a warning in Outlook 2007, see Macro to Warn Before Sending a Message with a Blank Subject
While not using a subject might increase the spam score a little, this warning was not added as an anti-spam measure. Some people do filter on a blank subject field, figuring any message without a subject is spam, but a subject is no guarantee the message is not spam.
This warning dialog was added because many users requested it.
It's good netiquette to include a subject, even if its just FYI as many people are annoyed when they receive messages without subjects.
Why do recipients want a subject? Because a subject helps them decide whether to read the message now or later. A subject also makes it easier to find messages when looking for a specific message. For example, if I need to find a message from Mary, I search for all messages from Mary. Because she uses subjects which generally reflect the content of the message, I can easily find the message I need just by viewing the list of messages. On the other hand, Jim rarely enters a subject so I need to look at each one of his messages until I find the one I'm looking for.
In Outlook when you have the Conversation view enabled, a subject will help messages create their own conversation as all of the no subject messages will group together as one conversation.
Please note: This feature is not at all related to MailTips. Users on some forums recommend changing MailTips settings to disable the No Subject warning dialog - this will not disable the No subject prompt, plus MailTips is an Exchange Server feature.