1) A public speaker who during his speech would like to quote verses from the written law, and finds it difficult to open the text and read from it each time, may say the verses by heart. (Mishne Berurah 49)
2) One may recite chapters from Psalms by heart, as it is like prayers in that it invokes Divine mercy, and furthermore there are those who permit all verses when not being used to fulfil other people’s duty, as mentioned above. (ibid)