General Readers
Gangopadhyay, M., Bhasabodhini: a Sanskrit Reader (Sri Garib Das Oriental Series) (1991, 2003) (held by the British Library, Niedersächsische Staats- und Universitätsbibliothek Göttingen, Universitäts- und Landesbibliothek Sachsen-Anhalt/Zentrale, Brigham Young University Harold B. Lee Library)
Brough, J., Selections from Classical Sanskrit Literature (1978)
(available to buy)
Mylius, K., Chrestomathie der Sanskritliteratur (1978, current imprint 2005)
(available to buy)
Warder, A. K., Sanskrit prose reader (1965) (3 vols: texts, vocabulary, notes)
pdfs of all three volumes will soon be available
Mahalinga Sastri, Y., A First Reader of Sanskrit (1947)
(held by: SOAS and the U of Hawai’i at Manoa)
Banerji, H.C, The New Method Sanskrit reader (1933)
(not available for download, held by: SOAS)
Böhtlingk, O., Sanskrit-Chrestomathie (1909)
(download: https://archive.org/details/sanskritchresto00bhgoog )
Liebich, B., Sanskrit-Lesebuch. Zur Einführung in die altindische Sprache und Literatur (1905)
(download: https://archive.org/details/bub_gb_uyMYAAAAYAAJ )
Liebich, B., Präparierheft zu Liebich Sanskrit-Lesebuch (1906)
(held by: Harvard College Library)
Lanman, C. R., A Sanskrit Reader (1883)
(download: https://archive.org/details/asanskritreader01lanmgoog )
Schmidt, J., Kleine Sanskrit-Chrestomathie (1868)
(download:
https://books.google.co.uk/books?id=ZznXmxwLBZIC&pg=PR1&lpg=PR1&dq=•+Johannes+Schmidt:+Kleine+Sanskrit-Chrestomathie.&source=bl&ots=7AzbQl3zZD&sig=2TFDr8XRqByIa4JxRqow8w9GIG4&hl=en&sa=X&ved=0ahUKEwigpMjlgtLUAhWe14MKHbCDBqAQ6AEILzAC#v=onepage&q=%E2%80%A2%20Johannes%20Schmidt%3A%20Kleine%20Sanskrit-Chrestomathie.&f=false )
Hoefer, A., Sanskrit‐Lesebuch mit Benutzung handschriftlicher Quellen (1849)
Readers with a focus on particular texts or genres:
Hock, H. H., An Early Upanishadic Reader (2006)
(available to buy)
Dhammajoti, B., Reading Buddhist Sanskrit Texts (2015?)
(not available as a pdf, currently no copies available for sale)
Gonda, J., A Sanskrit Reader, containing seventeen epic and puranic texts, with a glossary (1935) (held by: Universitätsbibliothek Würzburg, Universitätsbibliothek München, Bibliothek der Humboldt-Universität Berlin, Royal Danish Library - Copenhagen / CUL (DKB), Danish Union Catalogue and Danish National Bibliography)
Vedic Readers
Macdonell, A. A., A Vedic Reader for Students (1917)
(download: https://archive.org/details/vedicreaderforst00macd )
Hillebrandt, A., Vedachrestomathie (1885)
(does not seem to be available as a pdf online; available to buy as a modern reprint, held by various libraries)
Windisch, E., Zwölf Hymnen des Rgveda mit Sāyaṇa's Commentar (1883)
(download: https://archive.org/details/zwlfhymnendesr00sayauoft
Delbrück, B., Vedische Chrestomathie (1874)
(download: https://archive.org/details/vedischechresto01delbgoog )
Sanskrit ‘Readers’ that feature collections of texts in translation
J. F. Staal (ed.), A Reader on the Sanskrit Grammarians (1972)
(download: http://b-ok.org/book/2029976/428be2)
Kretschmer, H. Sanskrit Reader 1: A Reader in Sanskrit Literature (2015)
(print-on-demand, information: www.indische-bibliothek.de)