Few languages have a true one-to-one mapping of letter to phoneme. Spanish, for instance, has a pretty clear orthography, in that the spelling usually reflects the pronunciation, but the orthography isn't one-to-one: The most obvious example is the letters c and g, which are pronounced /k/ and /g/ before back vowels, but /θ/ (or /s/ in Latin America) and /x/ before front vowels. This also renders quite a few letters and digraphs redundant: qu /k/, gu /g/, and z /θ/ (and s /s/ in Latin America), j /x/, x /x/. Redundancy in an orthography means that orthography, however consistent it may be, isn't one-to-one. However, Spanish orthography is still easier to learn than English orthography, because there are fewer rules and exceptions you need to memorize to understand how to pronounce it. (A comparable case is modern Greek, in which all of ι, η, υ, ει, οι, υι are pronounced /i/, and yet the pronunciation is usually predictable from the spelling.)
French would be an extreme example of a (mostly) phonemic orthography that requires knowledge of a lot of rules. French orthography is mostly phonemic if you understand those rules (e.g., final unaccented e always being silent, etc.), but there are still exceptions that have to be memorized, such as femme /fam/ (not */fεm/), eu /y/ (not */ø/). English is also mostly phonemic, in that the pronunciation is usually predictable from complicated rules, but there are many more exceptions than in French.
There are many languages without a one-to-one mapping of orthography to spelling that are still mostly phonemic. However, most leave out some phonemic information.
In Ancient Greek, for example, there is no written difference between /a, i, y/ and /a:, i:, y:/. In Homeric Greek there was a phoneme /w/ that isn't indicated in the text of Homer that came down to us. Both /ei̯/ and /e:/ were written ει, and both /ou̯/ and /o:/ were written ου, despite being distinguished in pre-Classical Greek (see spurious diphthong). Tone stress is also not distinguished in early inscriptions and manuscripts. Latin doesn't distinguish any vowels by length; i can represent any of /i, i:, j/ and v can represent any of /u, u:, w/ (in later texts, /j/ is written j and /w/ is written v).
All abjads, by design, totally leave out information about vowels, and so languages that use them naturally aren't phonemic with regard to vowels. For example, in Hebrew, /a/ can be represented either by א or ה as matres lectionis, or by no letter at all. Hebrew is also ambiguous about consonants in the letter ש, which can be pronounced either /ʃ/ or /s/ (going back to an older ambiguity between /ʃ/ and /ɬ/ alongside ambiguity between /ħ/ and /x/, /ʕ/ and /ɣ/).
Finally, some languages that use syllabaries, such as Akkadian, have symbols with ambiguous phonemic values, because they can either represent a syllable or an ideogram. The symbol DINGIR in Akkadian could mean any of: the stem il-, the god Anum, the word šamû, the syllables an and il, a preposition meaning "at" or "to", or a determinative indicating that the following word is the name of a god (from Wikipedia), and of course the phonetic value would vary (or be absent) accordingly.
On the other hand, there are some languages that are closer to an ideal one-to-one orthography. Finnish has a nearly one-to-one orthography. The same is true of many languages whose orthographies were standardized recently. Wikipedia also has a list of languages which it describes as having a high grapheme-to-phoneme and phoneme-to-grapheme correspondence, which includes Serbo-Croatian, Bulgarian, Macedonian and others.