Yes, you should. You are attempting to sell yourself in some sense to recruiters and other people who are only casually interested.
There are many, many examples of retailers finding out that having a human picture increases conversion rates on their websites (meaning more product sold, etc).
For example: in this article customers were 10%-20% more likely to call when presented with a human picture. In web terms, this is a huge increase.
Additionally, a variety of examples indicate that images can increase conversion rate
Medalia Art sells Brazilian and Caribbean art online and using photos
of artists on their homepage increased conversions by 95%...
When they replaced the painting with actual photos almost doubled the
conversion rate (conversion in this case was clickthrough, not sales)
(this assumes of course you have a professional enough picture... don't put a picture of you at 2:00am after a night at the bars... at least for most professional jobs this probably would be worse)
There is a difference between a resume and a LinkedIn profile, by the way, in that LinkedIn tends to attract unsolicited interest this rarely occurs with a resume. You almost always submit your resume specifically to someone - you are initiating the contact. While with LinkedIn you have the opposite type of interest.