In English and many other languages I could say something like this:
Tom and Jack play football and baseball respectively.
That means that Tom plays football and Jack plays baseball.
How can I say this in German? What is the equivalent of "respectively"?
This is expressed with the conjunction beziehungsweise (often abbreviated bzw.) in the meaning und im andern Fall (in the other case).
Admittedly, the structure of a German sentence containing beziehungsweise is different from the structure of an English sentence containing and ... respectively. Rather than translating word by word, one replaces the conjunction and by the conjunction beziehungsweise. The adverb respectively is dropped, because it is already implicit in the conjunction beziehungsweise. For example, the sentence
Tom and Jack play football and baseball, respectively.
is translated to
Tom und Jack spielen Fußball beziehungsweise Baseball.
meaning that Tom plays football and Jack plays baseball.
ihre Tochter und ihr Sohn sind sechs beziehungsweise acht Jahre alt (her daughter and son are six and eight respectively). But this answers example could as well mean that Tom AND Jack play soccer AND baseball. I'm a native speaker.
Ich pflichte Björn Friedrich bei, dass
Tom und Jack spielen Fußball beziehungsweise Baseball.
die vorherrschende Form ist, derartiges auf Deutsch auszudrücken, möchte aber ergänzen, dass
Tom und Jack spielen Fußball, respektive Baseball.
auch nicht ganz ungebräuchlich ist, aber im Straßenjargon ist es sehr selten.
Baseline
While respectively typically translates to beziehungsweise, respektive or jeweils, neither seems optimal in your example. As @steros has pointed out in a comment, the translation ...
Tom und Jack spielen Fußball, respektive / beziehungsweise Baseball.
... suffers from a subject ambiguity that produces a reading in which both boys would play both sports. Pragmatics might filter this reading in the given example (for 'beziehungsweise' would suggest that both sports were related in some way, possibly to the extent that the latter were a specialization of the former, so since the relationship here is tenuous, the translation would probably work as intended). However, the preferred reading is much less pronounced if the sentence comes with very disparate leisure activities:
Tom und Jack spielen Fußball beziehungsweise Schach.
[Tom and Jack play football and chess, respectively.]
Note that the problem does not arise in a context that implies an ordering, as in
Tom und Jack wurden Dritter beziehungsweise Vierter.
[Tom and Jack ranked third and fourth, respectively.]
as different ranks cannot be held simultaneously.
Improvement
A better translation would be:
Tom spielt Fußball, respektive Jack Baseball.
which resolves any ambiguity though it still feels a bit odd - you'd rather express the contrast with a conjunction:
Tom spielt Fußball, Jack hingegen Baseball. / Während Tom Fußball spielt, spielt Jack Baseball. [Tom plays football while Jack plays baseball]
Caveat
All grammaticality assessments based on native-speaker intuition, no formal references.
jeweils? Tom und Jack spielen jeweils Fußball und Baseball. Although to be honest, I'd just say "Tom spielt Fußball und Jack spielt Baseball" without any extra complications.
jeweils include a meaning that partitions time into periods where exactly one of the given alternatives happen, ie. football and baseball being played, respectively ( scnr ;) ), by both boys. There also is the meaning that each of the boys plays football and baseball. To me that is the dominant reading right now, though it might be that I've become biased by considering the issue.
Commented
Sep 24, 2019 at 18:58
It is a common mistake when translations attempt to preserve the syntax of the source language. The correct question in the context of translation is not how one might translate the English construction X and Y do A and B respectively into German, but what a native speaker of German would say when they want to convey the same meaning. And what a native speaker of German would say is:
Tom spielt Fußball und Jack spielt Baseball is grammatically correct but would be considered poor style due to the doubling of the verb and of the sentence structure. In fact I've rarely run into communication by a native speaker that would not apply elision (whether orally or in writing): Tom spielt Fußball und Jack Baseball.
Commented
Sep 26, 2019 at 13:33
The weakness of a sentence like
Tom und Jack spielen Fußball, respektive / beziehungsweise Baseball.
is that it is not clear if it relates to "Tom and Jack respectively", or any other entity mentioned before. "Beziehungsweise" also means in german "more precisely" or "rather". I wouldn't use it in that way.
Although the answers of Björn Friedrich and user unknown are correct in giving good translations of respectively, it is not really common to use this construction to express two relations, especially if it contains potential ambiguity. The natural way to express this situation in German would be to completely let go the concept of respectively and use two connected main clauses.
In German, if you want to prevent the sentence from becoming too long and/or complicated, it is quite common to omit some words or parts of words that are not essential for understanding, so if Tom plays A and Jack plays B you omit the second "plays". Also most of the time "Fußball und Baseball" would be shortened to "Fuß- und Baseball".
So the most idiomatic translation of your sentence into German would be to abandon respectively and say:
Tom spielt Fuß- und Jack Baseball.
What about this version ?
Tom und Jack spielen entsprechend Fußball und Baseball
Mein Sohn und meine Tochter sind entsprechend sechs und acht Jahre alt
entsprechend cannot be used to disambiguate subject-object relationships. Rather it refers to a constituent outside the scope of the sentence proper, often establishing a causal relationship. Example: Hamburg ist eine Hochburg des Ballsports. Tom und Jack spielen entsprechend Fußball und Baseball. [Hamburg is a stronghold of ball sports. Tom and Jack play football and baseball accordingly], meaning that Tom and Jack do both sports).
Commented
Sep 25, 2019 at 9:18
The most common construction using "beziehungsweise" is explained in other answers. If you care for a similar sentence hierarchy to the English version, you can use
Tom und Jack spielen jeweils American Football und Baseball.
As a note aside: where "baseball" rather than "cricket" is a thing, "football" does not mean "soccer" and thus cannot be translated as "Fußball".