I'll count from Sverker the Elder 1134, as Before that, it is not proven that somone was King of Östergötland, Västergötland and Svealand at the same time - thus there was no Kingdom of Sweden, only a personal union between three Kingdoms (even if all three really were under one regent).
Sverker I 1134-1156 (Sverker Cornubesson).
Erik I 1156-1160 (Erik Jedvardsson, Erik the Holy).
Magnus I 1160-1161 (Magnus Henriksson).
Karl I 1161-1167 (Karl Sverkersson).
Knut I 1173-1196 (Knut Eriksson).
Sverker II 1196-1208 (Sverker Karlsson, Sverker the Younger).
Erik II 1208-1216 (Erik Knutsson).
Johan I 1216-1222 (Johan Sverkersson).
Erik III 1222-1229 (Erik Eriksson).
Knut II 1229-1234 (Knut Holmgersson).
Erik III 1234-1250 (Erik Eriksson).
Valdemar I 1250-1275 (Valdemar Birgersson).
Magnus II 1275-1290 (Magnus Birgersson).
Birger I 1290-1318 (Birger Magnusson).
Magnus III 1319-1364 (Magnus Eriksson).
Albrekt I 1364-1389 (Albrecht of Meckelburg).
Margareta I 1389-1396 (Margareta Valdemarsdotter, Queen of Denmark).
Erik IV 1396-1434 and 1435-1436 and 1436-1439 (Erik of Pommerania, King of Denmark).
Kristoffer I 1440-1448 (Kristofer of Bavaria, King of Denmark).
Karl II 1448-1457 (Karl Knutsson (Bonde)).
Kristian I 1457-1464 (Kristian of Oldenburg, King of Denmark).
Karl II 1464-1465 and 1467-1470 (Karl Knutsson (Bonde)).
Hans II 1497-1501 (Hans of Oldenburg, King of Denmark - Johan and Hans are considered the same name for Swedish regent numbering).
Kristian II 1520-1521 (Kristian of Oldenburg, King of Denmark).
Gustav I 1523-1560 (Gustav Eriksson (Vasa)).
Erik V 1560-1569 (Erik Gustavsson (Vasa), Erik XIV).
Johan III 1569-1592 (Johan Gustavsson (Vasa), Johan XIV).
Sigismund I 1592-1599 (Sigismund Johansson (Vasa), King of Poland).
Karl III 1604-1611 (Karl Gustavsson (Vasa), Karl IX).
Gustav II Adolf 1611-1632 (Gustav Adolf Karlsson (Vasa), Gustav II Adolf).
Kristina I 1632-1654 (Kristina Gustavsdotter (Vasa), Kristina I).
Karl IV Gustav 1654-1660 (Karl of Pfalz, Karl X Gustav).
Karl V 1660-1697 (Karl of Pfalz, Karl XI).
Karl VI 1697-1718 (Karl of Pfalz, Karl XII).
Ulrika Eleonora I 1718-1720 (Ulrika Eleonora of Pfalz, Ulrika Eleonora I).
Fredrik I 1720-1751 (Fredrik of Hessen, Fredrik I).
Adolf Fredrik I 1751-1771 (Adolf Fredrik of Holstein-Gottorp, Adolf Fredrik I).
Gustav III 1771-1792 (Gustav of Holstein-Gottorp, Gustav III).
Gustav IV Adolf 1792-1809 (Gustav Adolf of Holstein-Gottorp, Gustav IV Adolf).
Karl VII 1809-1818 (Karl of Holstein-Gottorp, Karl XIII).
Karl VIII Johan 1818-1844 (Karl Johan Bernadotte, Karl XIV Johan).
Oscar I 1844-1859 (Oscar Bernadotte, Oscar I).
Karl IX 1859-1872 (Karl Bernadotte, Karl XV).
Oscar II 1872-1907 (Oscar Bernadotte, Oscar II).
Gustav V 1907-1950 (Gustav Bernadotte, Gustav V).
Gustav VI Adolf 1950-1973 (Gustav Adolf Bernadotte, Gustav VI Adolf).
Karl X Gustav 1973-Present (Karl Gustav Bernadotte, Karl XVI Gustav).