UA now offers one-way award ticket booking, but doesn't allow stopovers.

Info from UA's one-way ticket overview:

The facts
• One-Way Awards are available for both Saver Awards (fewer miles) and Standard Awards (more miles and more flexibility).
• You can use these awards to fly United- or United Express-operated flights only. Sorry, these awards cannot currently be used with our airline partners.
• You must fly the most direct route from origin to destination. That means no stopovers. You can, however, make connections. Tip: If you want to visit multiple cities, you can use multiple One-Way Awards to create your itinerary.
• You can change your award ticket at any time or get a refund before you travel, but know that you may be charged a fee. See fee chart for details
• Complete One-Way Awards rules

Miles required
• The number of miles you’ll need will depend on your origin, destination and award level.
• You will need half the number of miles you would for a roundtrip award ticket.
• With a Saver Award, you’ll need fewer miles. With a Standard Award, you’ll need more miles, but will gain flexibility in dates and can book any seat that is available.
• When you use our award search, miles required will be indicated for each flight, but you can also refer to the One-Way Saver Awards or One-Way Standard Awards charts for a list of miles required by region.

http://www.united.com/page/article/0,6867,53338,00.html