I think mine is probably Monkey Island? I have 1-4 and Tales, plus the special editions of the first two (first one on Steam, second on XBLA) if you're going to count those separately.
In all honesty I don't think many of the other series I've played have that many instalments, at least not on the systems I owned. Partly that I went from PSX to Gamecube to Xbox360 (that last one only last year) with the consecutive Nintendo handhelds throughout when I was younger (GB, GBA, DS).
Thinking about it I *do* own a few Sonic games, though ironically none of them on any Sega platform - Sonic Advance, Sonic Adventure DX, Sonic Adventure 2, Sonic Heroes and Shadow the Hedgehog on Gamecube, plus Sonic 3 & Knuckles and the Sonic Mega Collection on PC. Though it's been quite some time since I last played any of those.
There are others that come close as well I suppose - Metroid (Prime 1 & 2, and Fusion); Mario (Mario Land 1 & 2 on Gameboy, Sunshine); Wario (Wario Land 1, 2 & 4, and Wario Ware (GBA and Wii))
....I think there are two rather telling things here. One, most of my game buying was done whilst I was on the Gamecube. Two, games on Nintendo platforms do have a shocking number of instalments which I had never quite considered.
Half-Life I suppose as well, but I only have 1, 2 and the episodes, not Blue Shift or OpFor (I think that's what they were called). Pretty much the rest is a random selection with few crossovers - with some exceptions of course, but if I were to list everything where I owned either two or three instalments I'd be here all day.