"J'aime le sport" is right but not "J'aime les voyages" (This latter is understandable but lacking in specificity1.) As an assertion of the same type, such as for instance "J"aime les livres.", "J'aime les plats cuisinés.", you'd get your meaning through more directly by saying "J'aime voyager.".
Sometimes the corresponding verb can be used; sometimes the meanings do not correspond; fairly often it's a matter of idiomatisme whether you use one form rather than another; I list a few cases below.
- J'aime voyager. (not "le voyage" but "les voyages" if less specific is possible)
- J'aime parler. _ J'aime la conversation. (neither "la parole" nor "l'élocution")
- J'aime penser. (neither "la pensée" nor "les pensées")
- J'aime plaisanter. _ J'aime la plaisanterie. _ J'aime les plaisanteries. (the sense is similar in this case)
- J'aime étudier. _ J'aime l'étude. _ (not "les études")
- J'aime cuisiner. _ J'aime la cuisine._ (not "les cuisines")
- J'aime lire. _ J'aime la lecture2 (also, but not as specific, "J'aime les livres." (not "le livre"))
- J'aime écrire. _ J'aime le travail de plume. (neither "l'écriture" nor "les écritures")
- J'aime tricoter. _ J'aime le tricot. (not "les tricots")
- J'aime coudre. _ J'aime la couture.
J'aime la peinture. _ (not "les peintures")
J'aime l'art. _ (not "les arts")
J'aime manger. _ (there is not really an equivalent with a noun: "J'aime la nourriture." is not something people would say in French; you may say it in English ("She likes food." or "She likes to eat.") ; in French you have to be specific as regards food ; J'aime les plats turks. _ J'aime les fruits de verger. _ J'aime la cuisine hispanique.)
1 Modification après considération de la remarque de jlliagre dans les commentaires
2Due to a correction by vaab in the comments