English is not one of those, while German should be. Italian is one of those and French is not. So it seems that this feature does not depend on the linguistic similarity and historical relation among languages. Or am I wrong?
For your question to make sense, it would have to be a question about particular language-orthography pairs (and if in talking about sound-symbol correspondences we interpret "sound" to mean "phoneme", then the question is further restricted to language-alphabet pairs, excluding syllabaries and logographic orthographies). So for example, you could ask whether the Roman alphabet as used to write Parisian French shows a 1:1 phoneme:grapheme relationship. If you're interested in syllabaries, you would ask whether a 1:1 mapping existed between graphemes and phonotactically legal syllable shapes in that language (syllabaries are by definition not 1:1 with regard to phonemes).
However, a further complication is that spoken languages change over time, and orthographies do not necessarily change along with them. As such, even if a particular language-alphabet pairing has a one-to-one correspondence of phonemes to graphemes at one point in time, there is no guarantee it will remain so.
As far as global patterns go, there is no systematic relationship between the orthography used to write a language and the genealogical history of that language. For example, lots of languages all over the world from all different language families use the Roman alphabet, and in many of those cases they do so because:
they had no orthography prior to contact with European anthropologists, linguists, and missionaries, and the development of their orthographies were strongly influenced by those Europeans, and/or
their orthographies are very recent and are designed to make easy use of language technology (like computers).
To give another example, the Mongolian script is used to write Mongolian, Evenki, and Xibe, but in principle could be adapted to write many other languages too. On the other hand, the Mongolian language is also commonly written using a slightly modified form of the Cyrillic alphabet.
If you insist on a strict reading of "one-to-one correspondence between sound and written symbol", there are actually very few, if any, well-known languages that qualify. Italian certainly doesn't: its writing system uses the letter H in words like "ho" and "hanno" where it doesn't correspond to any sound. German also certainly does not qualify: among other things, voiceless /f/ can correspond to either the letter V (as in Vater) or the letter F (as in Fall).
Languages with contrastive stress/pitch often leave that out, but it's a bit more arguable whether that qualifies as a violation of the principle of "one-to-one correspondence between sound and written symbol", since stress/pitch could be seen as a "non-segmental" element of pronunciation. Serbian, mentioned in Jelena's answer, apparently has phonemically contrastive vowel length that is not indicated in the spelling, which interacts in some way with a phonological pitch accent system (which also seems to be left out in the spelling).
If you relax the criteria, you get more of a spectrum. It is well known that for French, it's easier to predict pronunciation from spelling than it is to predict spelling from pronunciation. English is pretty tricky in both directions, but there are significant patterns. The elements of spelling systems that have less clear correspondences to pronunciation usually tend to be older.
A complete 100% one-to-one correspondence between the letters and the phonemes is Serbian language. In serbian there are two scripts Cyrilic and Latin but only in Cyrilic is one letter-one phonem. We have 30 letters and therefore 30 phonemes. Vuk Stefanović Karadžić reformated language in 1814. making ideal phonemic orthography.
I'd say that Esperanto is one of those languages. I don't remember a change in pronouciation possible.
The only exception maybe being the commonplace use of letter x, but this is due to limitation of computer keyoards about accents.
ĉ, ĝ, ĥ, ŝ, ŭcan be more easily written
cx, gx, hx, sx, uxknowing that the letter x is not exisiting at all in the normal esperanto alphabet.
I don't know if that count as a writting system since it is not the main one used in everyday life for chinese people. But the pinyin writting system, for transcribing pronunciation of Mandarin/Han Chinese, has a one-to-one correspondance between sounds and written form.
I was thinking about spanish: What you can read, you can pronounce it. But as a comment rightly highlighted there are much more exceptions in pronunciations than what I thought.
Exception with letter
- may be pronounced
s, according to a fixed rule on the following vowel.
l which becomes another sound when doubled into