Apparently is common, so I wanted to know just how much.
Sometimes people talk of sentential intonation as a kind of "stress", but Í would never do thàt. Still, including that phenomenon under the umbrella of stress, all languages have many degrees of "stress". Standardly, "stress" is a property of words, and excludes sentential intonation. Although many languages have some kind of stress (lengthening and pitch modulations are the basic phonetic exponents of stress), not all languages do. Some examples of languages without any degree of stress are Gen, Shua, Guerze and Matumbi: these are tone language. There has been a contrary belief that stress and tone are mutually incompatible properties, but there are enough languages documented with some form of "stress" (typically durational manipulations) that we can say that Zulu, Shambaa and various dialects of Chinese have both tone and stress. Demonstrated "stress" in a tone language is uncommon, and since up to a third of the world's languages are tonal, that would be a substantial source of possibly no-stress languages. French is the best-known examle of a language with neither tone nor word stress, though some people interpret the language as having final stress; Tigre is a similar less-known case.
Usually, it takes a fancy phonetic study to demonstrate that a language "has secondary stress", though you do find cases like English where it is a contrastive property and is easy to document (noun permit versus vomit). In Finnic languages, there does seem to be secondary stress (on every other syllable – it's rule-governed). But there is no evidence for secondary stress in quite a number of other languages, for example Kurdish, Arabic, Sundanese.
There are also languages which have multiple stresses within a word (a prerequisite for having primary versus secondary stress), but where no syllable is more prominent that the other. Tübatulabal and Waorani are described as having regular alternating stress but no difference in phonetic prominence between primary and secondary stresses.