In September, I'll be visiting family in North Carolina and Pennsylvania, spending three nights in each state. When I priced the tickets in June, I used two different approaches.
The multi-city flight, using ITA Software, with one round-trip ticket (Tucson to Raleigh to Philadelphia and back to Tucson) would have cost $821.50. Since ITA Software gives the prices for many airlines, I also checked the same round-trip ticket with the same multi-city routing and dates on an individual airline site--American Airlines. American Airlines gave me a figure of $844.40.
Next, I priced each segment as a one-way and found an amazing price difference. Three separate tickets cost the following: $159.80 on American Airlines for the Tucson to Raleigh flight and another $159.80 for the Philadelphia to Tucson flight. I also paid $138.90 for the Raleigh to Philadelphia flight using Delta Airlines. (The price for the RDU to PHL route was prohibitively expensive on American Airlines, but fairly reasonable on Delta. Since I was buying one-way tickets, it was easy to shop around for the best price for that segment.)
The total for my three one-way flights is $458.50 which is an astonishing $363.00 cheaper than the cheapest multi-city round-trip flight ITA was able to find.
I don't know if it is consistently cheaper to book one-way flights instead of a multi-city round-trip ticket, but I will always spend a few extra minutes to find out.
If you haven't used ITA Software yet, be sure to give it a try the next time you book a flight. While you can't actually purchase tickets on the site, it gives more information about options than any other site I know. You almost feel like a travel agent with all this information at your fingertips!
Note, too, that you can use ITA to find the best price on upcoming flights. For example, I just priced a flight from Raleigh to New York (JFK) in November and found prices ranging from $183 (mid-month) to $277 (beginning of the month and around Thanksgiving). When your dates are flexible, using this software is an easy way to find the cheapest time to fly.