The first U.S. census was in 1790 with the census being held every 10 years since. Census records that have been released to the public are maintained by the National Archives and Records Administration, not the U.S. Census Bureau. Census records are kept confidential for 72 years to protect the privacy of respondents (see why here) and records that have not been made public can only be obtained by the person named in the record or by their heir after submitting the proper form found here. Publications related to census data collected from 1790 to the most current census data are available at: https://www.census.gov/library/publications.html. They can also be found on different genealogy websites due to their free availability.
While the majority of information collected over the decades has not changed, details within the available records that are displayed may vary depending upon what was considered of importance at the time. You can see an example of this in the New York Times article, "An American Puzzle: Fitting Race in a Box" which discusses the changing ways that the U.S. census has collected and presented race.
For the most part, all census records that can be available to the public (once they have passed the 72 year rule) will be available to the public. However, damage to records such as fire damage to where records are stored may make certain years or sections unavailable.
There are many different ways to access census records. You do not need to use an online subscription (i.e., fee-based) service to access census records, although some free services may require that you create an account. If you would like to try one of the subscription services, many public libraries provide access to these to their patrons for free although some may require that you be in the building in order to use them.
Searching census records can be more of an art rather than a science. Census records are handwritten records that have been scanned into databases that have been transcribed, often by volunteers, interpreting the handwriting that greatly varies in quality. This means that even though you may be searching the correct name, your search may yield few results because the transcriber did not interpret the writing correctly. Additionally, if you are searching newly released records, your search may yield no results because these records have not been transcribed and only machine read and the machine has not interpreted the handwriting in a way that matches your search.
How can you work around this? One way to work around this frustrating aspect of dealing with census records is to utilize the location portion of the census records, if you can. However, be careful in using too much limiting information like full names or names where the spelling is particularly unique.
For example:
In the example shown above, I conducted a search in the 1950 census for "Hahn" in the state of "Iowa" in the county of "Fayette." These search terms yielded 2 results.* Within these results, you can see that the machine reading, struggles to interpret the handwriting with it combining Walter's first name and middle initial into Waltere. The machine reading software cannot interpret that the line designates a same household and therefore does not connect Ruth (or, as it reads, Buth) and Herbert are also Hahns who should have been part of my results list.
*At the time of this particular search, the 1950 census had only been available for 2 years meaning they were heavily relying upon machine reading and not volunteer transcription. Hence the low result yield despite the clear indication that there should be more results.
Let's compare this to a previous census records report that has been out for longer:
This record comes from the 1940 census and the searchability of this census is vastly increased due to the length of time that these records have been available. Due to this, it is easier to be more exacting in my search to find Herbert Hahn in the records rather than his brother Walter who was the only one that the records previous pulled out due to the machine's inability to read names and lines.
Census records, generally, are going to be looking for the same basic information. They are looking at residences, taking a count of the number of residents at that address, and gathering some data of the residents at that address. It is important to note that all of this information is self-reported and equally important that information is then recorded by another individual to the best of their ability. Spellings may be inaccurate, information may be misreported or misremembered.
How much does handwriting vary?
These two records are both part of the 1940 census making them contemporaries of each other and while the handwriting is similar, it is distinct. You can find a lot of variation across the records with some writing being more difficult to decipher than others.
As previously stated, all items in the census records are self-reported by a member of the household. Details may be misremembered or reported incorrectly by the household member that they are asking. Additionally, the recorder of the information may take correct information and transcribe it incorrectly.
Henry's wife is listed as "Tillie" in the 1930 census. If you were to search her full name (Ottillie), however, you would not be able to locate her in the census.
Meanwhile in the 1920 census, the recorder marks her name as "Tilly" with a 'y' this time.
It should be noted that this was transcribed as "Toby" and that is what will appear if the cursor hovers over the text. This will impact the searchability and means that if you search the 1920 census for "Tilly Hahn" you will not find anything because it has been incorrectly transcribed as "Toby Hahn."
These small changes are what lead to people "disappearing" in the census. It is less that they disappear in the census and more that the records are not consistent across the decades. (This is why it is important to make thorough notes at the beginning and during the research process.)
In addition to these problems with census records, there are also the issues caused by the census recorder themselves. For example:
Henry and Tillie's oldest child is recorded as what can be deciphered as "Alvin" despite her name being Irene--which you can see in later iterations of the census. (This particular census has other errors as well.) This would lead to questions regarding her name--did they change her name or did she change her name?--as well as cause difficulties for anyone searching for her in the census records as they would find a gap in the records.