Antipopes
1. Saint Hippolytus
2. Novatian
3. Felix II
4. Ursinus
5. Eulalius
6. Lawrence
7. Dioscorus
8. Theodore
9. Paschal
10. Contantine
11. Philip
12. John
13. Anastasius
14. Christopher
15. Boniface VII
16. John XVI
17. Gregory
18. Benedict X
19. Honorious II
20. Clement III
21. Theodoric
22. Albert
23. Sylvester IV
24. Gregory VIII
25. Celestine II
26. Anacletus II
27. Victor IV
28. Victor IV
29. Paschal III
30. Callistus III
31. Innocent III
32. Nicholas V
33. Clement VII
34. Benedict XIII
35. Alexander V
36. John XXIII-I
37. Felix V
For a half a millennium the Church was free from the plague of Antipopes, until 1958

38. John XXIII-II
39. Paul VI
40. John Paul I
41. John Paul II
42. Linus II
43. Pius XIII
44. Benedict XVI
45. And who is next?

Note only those who were elected are considered.  There are several other types of claimants to the Papacy at this time, which are not worthy of inclusion in this list.
The first are those appointed by some alleged apparition or Divine Intervention, such as two of the Gregory XVII's, Clemente and Gaston Tremblay. 
Next there is a considerable number of internet fictions who only live on fake websites or in paint.  And some of these are quite elaborate ruses meant to deceive.  And finally there is the claim that someone other than Roncalli was elected in 1958.  Some say Cardinal Ottaviani and others claim Cardinal Siri.  However, there is no evidence to make either claim worth investigation.