As an information I have longer lists :
players who played at least 4 semifinals in the open era :
Federer 32 Connors 31 Lendl 28 Agassi 26 Sampras 23 Nadal-McEnroe-Edberg 19 Becker 18 Djokovic-Borg 17 Wilander 14 Rosewall 13 Vilas 12 Murray-Courier 11 Newcombe-Ashe-Roddick 10 Roche-Chang-Hewitt-Gerulaitis 8 Safin-Rafter-Ivanisevic 7 Laver-Nastase-Kodes-Stich-Kafelnikov-Ferrero-Martin-Tanner-Henman 6 Smith-Okker-Cash-Nalbandian-Kriek 5 Mecir-Leconte-Muster-Bruguera-Gimeno-Orantes-Solomon-Krajicek-Pioline-Grosjean-Tsonga-Davydenko-Ferrer-Haas 4
players who played at least 7 quarterfinals in the open era :
Connors 41 Federer 38 Agassi 36 Lendl 34 Sampras 29 McEnroe-Edberg 26 Nadal-Becker 23 Djokovic 22 Borg 21 Wilander 20 Vilas-Roddick 19 Newcombe 18 Rosewall-Ashe-Courier-Hewitt 15 Murray-Ivanisevic 14 Chang-Kafelnikov 13 Nastase-Roche 12 Gerulaitis-Tanner-Kriek-Okker 11 Smith-Kodes-Noah-Stich-Martin-Henman-Nalbandian-Davydenko 10 Safin-Ferrero-Ferrer-Grosjean-Krajicek-Muster-Cash-Leconte-Mayotte-Ramirez 9 Orantes-Kuerten-Moya-Tsonga-Pioline-Metreveli 8 Laver-Del Potro-Rafter-Mecir-Haas-Gonzalez-Björkman-Dibbs 7
if you see somebody missing from my lists, please tell me
(Rios and Corretja played 6 quarterfinals : if you have an extensive list of players having played 6 quarterfinals in the open era I would be grateful
)
and while I'm in that here should be the list of
players having played at least 3 finals
Federer 24 Lendl 19 Sampras 18 Nadal-Borg 16 Connors-Agassi 15 McEnroe-Edberg-Wilander 11 Becker 10 Djokovic 9 Rosewall-Vilas 8 Courier-Newcombe 7 Laver 6 Murray-Ashe-Nastase-Kodes-Roddick 5 Hewitt-Safin-Rafter-Chang-Ivanisevic 4 Roche-Smith-Gerulaitis-Cash-Stich-Kafelnikov-Kuerten-Bruguera-Ferrero 3