A lot of times, the person providing the information that goes on the death certificate doesn't know the exact information, so either makes a best guess, or doesn't know. (I know this because when my father died, they requested a piece of information, and my mother and I looked at each other with a totally blank expression, and then I remembered what was needed. But if we'd been unable to find it in our memories, it would have gone unrecorded.)
SeekingMichigan.org is a favorite free site of mine for Michigan research. They've got a wonderful collection of digitized death records from 1897 to 1920, civil war photographs and service records, WPA property inventories, maps, and naturalization indexes.
raogk.org - If you just need a single record, a copy of a newspaper obit, or a headstone photo, it's a good resource, although it's entirely hit-or-miss. Some volunteers are very prompt in responding. Some respond at first to say they'll execute the task but you never hear from them again. It's always worth a shot, just to see if you'll get lucky. And it's good karma to sign up as a volunteer.
findagrave.com - An incredible resource for both cemetery records, transcriptions and photos. It's on my checklist for every person's record I look up.
interment.net - Listing of cemetery transcriptions. Not as good as findagrave, and the navigation is more difficult to find what you want, but I always check it after I've been to findagrave because sometimes you get lucky.
books.google.com - Google Books can be an AMAZING resource for county and family histories, and often you can download a PDF of the entire book. I always check it before I order from Higginson books.
If you're organized but short on money, it's worthwhile to sign up for some of the fee-based resources for a trial period, or just a one-month period, then get everything you can from them during that period. These sites include newspaperarchive.com and footnote.com.
Keep in mind that many online resources (like ancestry.com, footnote.com and newspaperarchive.com) are available for free at LDS Family History centers. You need only pay the printout fee for copies.
And never underestimate the power of Google. When I go over records I've previously researched, I always google again to see if anything new has been indexed. I've unearthed some invaluable info by re-googling, including extensive family history info and photos.
Free: Follow a number of Genealogy Blogs. You never know what you might find.
Free: Have a Blog (or two) and have already connected to a couple of cousins. Ones that I have not connected with before.
Free: Find-A-Grave for for research and to contribute to
Free: When its time to consider an online Subscription, I use liveroots.com and see what pay for subscription provides hits. I also use it during my normal research. An added benefit, that it can be used from Second Life.
Free: Second Life is another resource. There are regularly scheduled Chats that cover a wide range of topics. Talking about "brick walls" comes up frequently. There is a great community of Family Researchers that participate in the Chats.