A Simple List of Roman Emperors

Ruled over the whole empire (more or less).

Augustus 27 BC - 14 AD
Tiberius 14 - 37
Caligula 37 - 41
Claudius 41 - 54
Nero 54 - 68
Galba 68 - 69
Otho 69
Vitellius 69
Vespasian 69 - 79
Titus 79 - 81
Domitian 81 - 96
Nerva 96 - 98
Trajan 98 - 117
Hadrian 117 - 138
Antoninus Pius 138 - 161
Marcus Aurelius 161 - 180
Lucius Verus 161 - 169
Commodus 177/180 - 192
Pertinax 193
Didius Julianus 193
Septimius Severus 193 - 211
Caracalla 198/212 - 217
Macrinus 217-218
Elagabulus 218 - 222
Severus Alexander 222 - 235
Maximinus 235 - 238
Gordian I and II 238
Balbinus and Pupienus 238
Gordian III 238 - 244
Philip the Arab 244 - 249
Decius 249 - 251
Gallus 251 - 253
Valerian 253 - 260
Gallienus 254 - 268
Claudius Gothicus 268 - 270
Aurelian 270 - 275
Tacitus 275 - 276
Probus 276 - 282
Carus, Carinus, Numerian 282 - 285

From Diocletian to Constantine the Imperial office was shared. Not all Tetrarchs are listed.
Diocletian 284 - 305
Maximian 286 - 305
Constantius Chlorus 305 - 306
Galerius 305 - 311
Licinius 311 - 324
Constantine 307 - 337
Constans I 323 - 350
Constantine II
Constantius II 324/337 - 361
Julian 361 - 363
Jovian 363 - 364
Valens 364 - 378
Theodosius 379 - 395

Ruled over the western half of the empire.

Honorius 395 - 425
Valentinian III 425 - 455
Majorian 457 - 461
Romulus Augustulus 475 - 476
Julian Nepos 476 - 480

Ruled over the eastern half of the empire.

Arcadius 395 - 408
Theodosius II 408 - 450
Marcian 450 - 457
Leo I 457 - 474
Leo II 474
Zeno 474 - 491
Anastasius 491 - 518
Justin 518 - 527
Justinian 527 - 565
Justin II 565 - 578
Tiberius II 578 - 582
Maurice 582 - 602
Phocas 602 - 610
Constantine III 641
Heraclius 610 - 641
Heracleonas 641
Constans II 641 - 648
Constantine IV 668 - 685
Justinian II 685 - 695
Leontius 695 - 698
Tiberius III 698 - 705
Justinian II 705 - 711
Bardanes 711 - 713
Anastasius II 713 - 716
Theodosius III 716 - 717
Leo III 717 - 741
Constantine V 741 - 775
Leo IV 775 - 780
Constantine VI 780 - 797
Irene 797 - 802
Nicephorus 802 - 811
Stauracus 811
Michael I 811 - 813
Leo V 813 - 820
Michael II 842 - 867
Theophilus 829 - 842
Michael III 842 - 867
Basil I 867 - 886
Leo VI 886 - 912
Alexander 886 - 913
Constantine VII Porphyrogenitus 912 - 959
Romanus I 919 - 944
Romanus II 959 - 963
Basil II 963 - 1025
Constantine VIII 963 - 1028
Nicephorus II 963 - 969
John I Tzimisces 969 - 976
Romanus III 1028 - 1034
Michael IV 1034 - 1041
Michael V 1041 - 1042
Zoe, Theodora 1042
Constanine IX Monomachus 1042 - 1055
Theodora 1055 - 1056
Michael Stratioticus 1056 - 1057
Isaac I Comnenus 1057 - 1059
Constantine X Ducas 1059 - 1067
Romanus IV Diogenes 1067 - 1071
Michael VII Ducas 1071 - 1078
Nicephorus III Botaniates 1078 - 1081
Alexius I Comnenus 1081 - 1118
John II 1118 - 1143
Manuel 1143 - 1180
Alexius II 1143 - 1180
Andronicus 1183 - 1185
Isaac II 1185 - 1195
Alexius III 1195 - 1203
Isaac II 1203 - 1204
Alexius IV 1203 - 1204
Alexius V Ducas Murtzuphius 1204
Theodore I Lascaris 1204 - 1222
John III Ducas Vatatzes 1222 - 1254
Theodore II Lascaris 1254 - 1258
John IV Lascaris 1258 - 1261
Michael VIII Palaeologus 1259 - 1282
Andronicus 1282 - 1328
Michael IX 1293 - 1320
Andronicus III 1328 - 1341
John V 1341 - 1376
John VI 1341 - 1354
Andronicus IV 1376 - 1379
John V 1379 - 1391 (Restored)
John VII 1390
Manuel II 1391 - 1425
John VIII 1425 - 1448
Constantine XI Dragases 1449 - 1453

Depending on your perspective, Constantinople either falls to or is liberted by the Turks.