Long, long ago, Tama-yori-hime, daughter of the Sea God, had a child with Hiko-nagisa-ta u-gaya-fuki-ahezu no Mikoto. They named him Kami-Yamato-Ihare-Biko. He was the first Emperor of Japan or Tenno, under the name of Jimmu. Here is his lineage.

Early Periods

The dates for the first emperors should not be taken too seriously. Consider how long most of the reigns are.

Emperor Jimmu          660-585 B.C.
Emperor Suizei         581-549 B.C.
Emperor Annei          549-511 B.C.
Emperor Itoku          510-477 B.C.
Emperor Kosho          475-393 B.C.
Emperor Koan           392-291 B.C.
Emperor Korei          290-215 B.C.
Emperor Kogen          214-158 B.C.
Emperor Kaika          158-98  B.C.
Emperor Sujin           97-30  B.C.
Emperor Suinin     29 B.C.-70  A.C.
Emperor Keiko           71-130       
Emperor Seimu          131-190      
Emperor Chuai          192-200      
Regent Jingu Kogo      201-269      
Emperor Ojin           270-310       
Emperor Nintoku        313-399    
Emperor Richu          400-405      
Emperor Hanzei         406-410     
Emperor Ingyo          412-453      
Emperor Anko           453-456       
Emperor Yuryaku        456-479    
Emperor Seinei         480-484     
Emperor Kenzo          485-487      
Emperor Ninken         488-498     
Emperor Buretsu        498-506    
Emperor Keitai         507-531     
Emperor Ankan          531-535      
Emperor Senka          535-539      
Emperor Kimmei         539-571     
Emperor Bidatsu        572-585    
Emperor Yomei          585-587      
Emperor Sushun         587-592     
Empress Suiko          592-628      
Emperor Jomei          629-641      
Empress Kogyoku        642-645    
Emperor Kotoku         645-654     
Empress Saimei         655-661     
Emperor Tenji          662-671      
Emperor Kobun          671-672      
Emperor Temmu          673-686      
Empress Jito           690-697          
Emperor Mommu          697-707         
Empress Gemmei         707-715        

Nara period

Empress Gensho         715-724        
Emperor Shomu          724-749         
Empress Koken          749-758         
Emperor Junnin         758-764        
Empress Shotoku        764-770       
Emperor Konin          770-781         
Emperor Kammu          781-806

Heian period

Emperor Heizei         806-809        
Emperor Saga           809-823          
Emperor Junna          823-833         
Emperor Jimmyo         833-850        
Emperor Montoku        850-858       
Emperor Seiwa          858-876         
Emperor Yozei          876-884         
Emperor Koko           884-887          
Emperor Uda            887-897           
Emperor Daigo          897-930         
Emperor Suzaku         930-946        
Emperor Murakami       946-967      
Emperor Reizei         967-969        
Emperor En-Yu          969-984         
Emperor Kazan          984-986         
Emperor Ichijo         986-1011       
Emperor Sanjo         1011-1016       
Emperor Go-Ichijo     1016-1036   
Emperor Go-Suzaku     1036-1045   
Emperor Go-Reizei     1045-1068   
Emperor Go-Sanjo      1068-1072    
Emperor Shirakawa     1072-1086   
Emperor Horikawa      1086-1107    
Emperor Toba          1107-1123        
Emperor Sutoku        1123-1141      
Emperor Konoe         1141-1155       
Emperor Go-Shirakawa  1155-1158
Emperor Nijo          1158-1165        
Emperor Rokujo        1165-1168      
Emperor Takakura      1168-1180    
Emperor Antoku        1180-1183      

Kamakura period

As the Heike Monogatari says, Emperor Antoku died at the battle of Dan-no-ura, which ended the Heike wars. Then Go-Toba, who was a 4-year-old child, became emperor. He appointed Yoritomo as Shogun. The relationship between the emperors, the retired emperors and the shoguns were very complex, so the following lists are only approximations.

      Emperors                            Shoguns
                                            
Emperor Go-Toba      1183-1198       Minamoto Yoritomo  1192      
Emperor Tsuchimikado 1198-1210       Minamoto Yoriiye   1202   
Emperor Juntoku      1210-1221       Minamoto Sanetomo  1203   
Emperor Chukyo       1221                                     
Emperor Go-Horikawa  1221-1232       Fujiwara Yoritsune 1226  
Emperor Shijo        1232-1242       
Emperor Go-Saga      1242-1246       Fujiwara Yoritsugu 1244
Emperor Go-Fukakusa  1246-1249       Munetaka-Shinno    1252     
Emperor Kameyama     1259-1274       Koreyasu-Shinno    1266     
Emperor Go-Uda       1274-1287       
Emperor Fushimi      1288-1298       Hisaakira-Shinno   1289    
Emperor Go-Fushimi   1298-1301       Morikuni-Shinno    1308     
Emperor Go-Nijo      1301-1308       Morinaga-Shinno    1333     
Emperor Hanazono     1308-1318       Narinaga-Shinno    1334     

Ashikaga period

Go-Daigo, who became emperor in 1318, tried several times to wrest power from the shoguns. He failed, but the Kamakura dynasty collapsed and was replaced by the Ashikaga dynasty. During several decades, there were also two rival emperors.

                  Emperors                             Shoguns

Southern Dynasty           Northern Dynasty              

Go-Daigo    1318-1338      Kogon      1331-1333     Takauji     1338
Go-Murakami 1339-1368      Komyo      1336-1348     Yoshiakira  1358
                           Suko       1348-1351     Yoshimitsu  1367
                           Go-Kogon   1352-1371     Yoshimochi  1395
Chokei      1368-1383      Go-Enyu    1371-1382     Yoshikazu   1423
Go-Kameyama 1383-1392      Go-Komatsu 1382-1392     Yoshinori   1428
                                                    Yoshikatsu  1441
                                                    Yoshimasa   1449
                                                    Yoshihisa   1474
Emperor Go-Komatsu      1392-1412                   Yoshitane   1490
Emperor Shoko           1412-1428                   Yoshizumi   1493
Emperor Go-Hanazono     1429-1464                   Yoshitane   1508
Emperor Go-Tsuchimikado 1465-1500                   Yoshiharu   1510
Emperor Go-Kashiwabara  1500-1526                   Yoshiteru   1545
Emperor Go-Nara         1526-1557                   Yoshihide   1568
Emperor Ogimachi        1557-1586                   Yoshiaki    1568

Azuchi-Momoyama period

Emperor Giyozei 1586-1611

Edo period

             
          Emperors                             Shoguns

Emperor Go-Mizuno-O    1611-1629            Iyeyasu    1603         
Empress Meisho         1630-1643            Hidetada   1605     
Emperor Go-Komyo       1643-1654            Iyemitsu   1622     
Emperor Go-Sai-In      1656-1663            Iyetsuna   1651     
Emperor Reigen         1663-1687            Tsunayoshi 1680   
Emperor Higashiyama    1687-1709            Iyenobu    1709      
Emperor Nakamikado     1710-1735            Iyetsugu   1713     
Emperor Sakuramachi    1735-1747            Yoshimune  1716    
Emperor Momozono       1747-1762            Iyeshige   1745     
Empress Go-Sakuramachi 1763-1770            Iyeharu    1760      
Emperor Go-Momozono    1771-1779            Iyenari    1786      
Emperor Kokaku         1780-1817            Iyeyoshi   1837     
Emperor Ninko          1817-1846            Iyesada    1853      
Emperor Komei          1847-1866            Iyemochi   1858     
Emperor Meiji          1867-1912            Yoshinobu  1866

Modern period

Emperor Taisho           1912-1926
Emperor Hirohito (Showa) 1926-1989
Emperor Akihito (Heisei) 1989

I used http://www.sho-shin.com/soverns.htm, and a couple of other partial sources as well. Thanks to gn0sis and sekicho, and a huge thanks to mauler for numerous helpful corrections.