Yes, many people say that genealogy is just dull and boring because of its focus on the vital statistics of births, marriages, and deaths. But how else do you think lawyers determine who can inherit, other than via family relationships and the closeness of them—in terms of blood, not emotional connection—in place of a will that doesn't exist? Your state probably has an intestacy law, meaning, without a will. You can leave your money to the dog if you wish, but in the absence of a will stating your last wishes, there are usually rules which establish who can inherit (note to self: spend down to the last five cents, and save everyone a lot of trouble!). So vital records are relied upon to prove relationships.
How do you find vital records of births, marriages, and deaths—these sine qua nons (without which nothing's)—of genealogical research, other than through your own or a library subscription to commercial databases? No, Virginia, it's not all online; these are often compiled records, not the original certificates.
There are other places to look for the actual certificates that can cover time periods differing from what the clerks in the registry offices tell you.
Recently, I had the occasion to work with a young Hispanic woman, whose parents and grandparents are deceased. Because of that, she does not have the family access of many 20 year-olds. We looked at old census records, which in Puerto Rico is all in Spanish and shows the father's name (A y B), the y being the "and" of the compound name; mother (C y D); and the kids (A y C). This shows both parents paternal "maiden" names in the names of any individual. That's not the date information we were seeking, but it does give us the names to look back for each generation.
Census materials can also help African-American researchers. Yes, slavery existed before the Emancipation Proclamation of 1863. But we recently found what we feel is the family of a black researcher, not with names, but with exactly matching ages. They appear on a list of slaves owned by a family in Georgia who had the same name as the black persons. It is possible—and needs to be confirmed independently—that the people there took the name of the plantation where they worked, after the Civil War. But the ages and numbers of people by age and gender match up exactly with later free censuses of the family. This data helps to confirm ante-bellum status. I didn't say this census proves that they are the right people—but it provides useful clues.
Newspaper indexes are another source. In our area, we were settled for all intents and purposes about 1810, and first incorporated in 1818. No directory exists until 1827. And the first cemetery records (using writer's license here) only start with 1837. So that's deaths from 1837. But there are many newspaper indexed entries for marriages and deaths. We almost never have found any births indexed, and only in the daily papers of the 1940s do we see lists of children born, and those can appear literally months after the birth. One of the local papers that is indexed gives reference to people being married or dying in Massachusetts and Ohio, which are 400 miles away from us. Of course they had a local connection, but that's a good thing if you are researching those families.
Newspaper articles from all time periods, as mentioned, are informative. One of my favorites is from the 1950s and tells of a woman who had 13 children, in multiple births. Today you could not get away with writing in the kind of dismissive attitude that article used, but the key thing is it had a picture, the residence, and the names and birth dates of all 13 children, plus the parents and grandparents mentioned.
Probate, surrogates, or will records often give the names and relationships, and often the places of residence of surviving family members. This can help by giving ages and places of residence of these people.
Librarians often use what we call "mug books." These are centennial or sesquicentennial publications (1876 or 1926 for the U. S. Declaration of Independence), where various people in a community are profiled and pictured, along with various vital data of birth, marriage, and death. Another recent example was a prominent businessman who fell into the time period not easily indexed. We found a mug book picture that mentioned he had been married three times, with all of the pertinent data, and that he had no children with any of the wives.
We also have sheriff and police arrest records in manuscript books from the 19th century. They could well give ages and birthplaces.
It goes without saying that church records are vital (pun intended). The earliest I have seen here are 1807, in a rural area, and that predates the official beginning of vital record keeping by more than 70 years, and the partial record-keeping of the 1840s by 40 years. As well, they may contain records of those who were born or married here and then moved elsewhere. Those who died here, naturally, tended to stay after their decease. One caution is that these records may have been filmed by the LDS Church (and so are available without traveling to the church here), but some were transferred to a local college, while others were sent to the archives at the state capital 60 years ago. I am sure this experience has been replicated all over the country. The records you seek could well be at the other end of your state. (This happens overseas, too, with my research in Germany sometimes leading me quite a few miles from the original church to a regional state archives).
A few other sources where I have seen vital data mentioned is the U. S. Census (rare, but occasionally you find exact dates, especially in the mortality lists); in naturalization papers, where the person told exactly where and when they were born overseas. These are much less likely to contain all that you want from vital records information but they certainly are worth a try.