Not many records will directly address the question of what languages your ancestors spoke. One notable exception is census records. The U.S. censuses provide two relevant types of information.
The first type of information is direct; censuses in some years provide explicit information about language. Both the 1920 and 1930 Censuses ask for the mother tongue or native language of foreign-born individuals, while the 1920 Census also asks for information about the mother tongue of foreign-born parents. Take my 2nd great grandmother Mary (Runiger) Kingsbury. She was born in Ohio, so her mother tongue is not listed in the 1920 Census, but her father was born in Switzerland and her mother was born in Germany, so their mother tongues are listed here as German.
The language spoken by an individual may also be listed in the 1910 and 1890 Censuses, but only if he or she does not speak English. My 2nd great grandfather, Paul Schoendorf, was born in Germany and spoke German, but also spoke English, so his mother tongue, German, is not listed in the 1910 Census.
In contrast, his mother tongue is listed as German in both 1920 and 1930.
Make sure that you know what is being asked. Read the column headings and the census instructions, which can be found on the Census Bureau website (here).
Place of Birth
The second type of information is more indirect. All censuses since 1850 have asked about the place of birth of individuals and every census from 1880 to 1930 lists the places of birth of both the father and mother of the individual. The place of birth can be an important clue to what languages your ancestors spoke. This is also a case where it is useful to check out the the census instructions. There are very specific instructions about how to list places of birth. For example, the 1910 instructions direct the enumerators not to list "Poland" but instead either "Germany (Pol.)", "Austria (Pol.)" or "Russia (Pol.)".
Keep in mind that there are limitations to using the census. First, not all enumerators followed the instructions very well. In some cases, this can be to your advantage; they may add more specific information than requested by the census. In other cases, this may mean incorrect information; they may have incorrectly assumed the language of individuals in the census or simply not understood the person being interviewed.
Second, information, especially about parents, may be incorrect. Your ancestors may not have known this information or may have had some reason to give false information. You may have an ancestor where the place of birth of a parent seems to change with every census. However, don't immediately assume that the information is false; there may be important clues even when the information is inaccurate or inconsistent. For example, for my 2nd great grandfather, Alfred Eugene Madison, his father's place of birth is listed as New Brunswick (C. Fr. [Canada French]) in 1900, Can. English in 1910, and Scotland in 1920. Of course, the last census is not compatible with the earlier ones, but maybe this indicates something about his ancestry.
Finally, the place of birth only tells us what languages our ancestor may or most likely would have spoken. No country is purely monolingual and there are always linguistic minorities. Remember that place of birth is only a clue, it's not direct evidence.