Binoculars are a great way to get started in observational amateur astronomy. These instruments are relatively inexpensive amd are eminently portable and easy to use. A surprising number of celestial objects including many binary stars, open and globular star clusters, nebulae, and even some galaxies can be detected with binoculars. Scanning through the heart of the Milky Way with binoculars from a very dark site is a truly fantastic experience.
I recommend purchasing a 10x50 (i.e., 10 power and 50mm aperture) binocular for astronomical use. Celestron, Nikon, Orion, and Pentax are good mid-price brands to consider. A 10x50 binocular is usually not overly heavy for most people to hand-hold and provides a 5mm exit pupil that will be appropriate for most observers when age and observing site darkness are taken into account. Information on binoculars suitable for astronomical observing can be found at the following sites:
Binocular Astronomy by Craig Crossen and Wil Tirion (which is out of print, unfortunately), Touring the Universe through Binoculars by Phillip Harrington, and Binocular Highlights by Gary Seronik are three excellent books on observing with binoculars.
Phil Harrington also writes a monthly binocular observing column for Astronomy. He also has binocular tours posted on his website and the Astronomy website. Phil's TUBA (Touring The Universe Through Binoculars Atlas) binocular planetarium program is available as a free download here.
This website discusses a number of deep-sky objects that can be seen through binoculars. A few more good objects are mentioned at http://www.backyard-astro.com/deepsky/bino/homeb.html
A list of binocular objects is included with each monthly Evening Sky Map at http://skymaps.com/downloads.html
The Astronomical League's Binocular Messier, Deep Sky Binocular, and Southern Sky Binocular lists include many of the best binocular deep-sky objects: