Finding old obituaries should be easier than it is. The information is all out there, and a great deal of it is digitized (and much of that is even free). The problem, though, is that it's often hard to tease out obituaries from other newspaper articles. The Washington Post archives, for instance, allow you to restrict searches to editorials, the sports section, etc...but there's no obituaries-only search. For some fairly unusual family names, this may not be much of an obstacle, but for more common names, it can be a real P.I.T.A., if you know what I'm saying.
A good resource to know about is the Obituary Archives. This isn't a deep historical resource, but for deaths that occurred from about the late 1970's on, it's a good, quick way to identify available online obituaries.
As is the case at many search sites, the initial search is free. Enter a name and other related information, like a range of dates, or a place, and you'll quickly get results that show you the name of the deceased, the date of the obituary, the newspaper in which it appeared, and often, a headline with a bit more information (Robert Smith, Inventor of Bubble Gum, or some such headline).
Obits are fascinating, but not always pretty
You'll have to pay to see the actual article, of course. You can view individual articles at $2.95 a pop, or get a monthly subscription to the site. These are text-only articles, so don't expect any photos, or actual page images.
One nice feature of ObitsArchive deserves mention. They include useful examples of searches you can enter in each field, like this...Name of Deceased: (William OR Bill) Smith. These are so incredibly helpful to first-time users of a site. I'm amazed (and a bit appalled!) at how many search sites don't manage to offer this simple assistance.
Give ObitsArchive a visit for death notices from the past few decades.
Visit the main page of Free Genealogy Tools for more, umm, free genealogical tools.
And don't forget to also check for your family history at Ancestry.com and NewspaperArchive.com. These are subscription databases, but they are among the most powerful research tools available for finding obituaries and looking into family roots.