Uhmm, interesting question. Are we counting remasters? Doesn't matter, I'll just count everything from originals to remasters and from things played indefinitely to things played only once. For series off the top of my head where I played 5 or more games. Hadn't seen this thread before, but let me count, and bear with me on the abbreviations lol 
;
Mario (platforming) - 16
MB, SMB, SMB2, SMB3, SML, SML2, SMW, SMA*, SMBDX, SM64, SMS, SMA4, SMG, SMG2, SM3DL, SM3DW
Mario (everything) - 34
(All of above plus) SMW2, SMA3, YIDS, LM, LM2, CTTT, SMK, MK64, MKDD, MKSC, MKDS, MKWii, MK7, MK8, MP, MP2, MP5, MP8.. and I think that's it, but maybe I'm forgetting something...
Star Wars - 33
SWA(Atari computer port), SW(NES), SWTPM, SWJPB, SWR, SWRotS, LSW, LSWII, SWRA, SWRAII, SWXWvsTF, SWRS, SWRSIII, SWDF, SWJK, SWJKMotS, SWJKII, SWJA, SWBF(2004), SWBFII(2005), SWKotOR, SWKotORII, SWTFU, SWTFUII, SWGB, SWEaW, SWSotE, SWMoTK, SWYS, SWBH, SWRC, SWLA, SWPD.. lol d*mn.
The Legend of Zelda (main series) - 25
LoZ, AoL, ALttP, LA, LADX, OoT, MM, OoA, OoS, FS, OoTMQ, TWW, ALttP/FS, TMC, TP, PH, ST, OoT3D, SS, TWWHD, ALBW, TPHD, MM3D, TH, BotW.. so everything and everything's remaster except FSA and the NES GBA ports.
The Legend of Zelda (everything) - 27
(All of the above plus) FPTRRL, HW.. have Crossbow Training, but never played it.
Sim - 10
SC, SC2000, STower, STown, SoSC, SC3000, TS, SC4, TS2, SCS
Guitar Hero - 6
GHIII, GHWT, GHM, GHOTD, GH5, GH6
Total War - 5
R:TW, MII:TW, E:TW, N:TW, TW:RII
Uncharted - 5
UDF, U2AT, U3DD, UGA, U4ATE
So I guess, Mario wins, being barely ahead of Star Wars with 34 against 33, if you take everything in a franchise together. Solely looking at consistant series though, the win easily goes to The Legend of Zelda, unsurprisingly.
Except when measured in time, then my most played series is probably Rollercoaster Tycoon, solely because of Rollercoaster Tycoon 2.
