I basically "owe" the start of my PC gaming journey to the following series (and specific titles within the series):
º Ultimate DOOM
More Ultimate DOOM than DOOM II, or Final DOOM. But ultimately Ultimate DOOM (ultimate, how many times will this word pop in this paragraph I don't know) was the original PC game that "brought me" to PC gaming, or rather that brought PC gaming to me. I guess that both ways work. I really can't remember the first time I played Ultimate DOOM, but it was probably sometime in 1994 or 1995 (at the time I think DOOM II had already been released).
I was still a console gamer and only got my actual first PC in early 2000 (it was my first PC ever to start with), and my first real "gaming-capable PC" in summer 2001. But even though I was gaming on consoles at the time I could never stop thinking about "that game I just saw at the local store called DOOM". That day, and that game marked me forever. It was as though there was a big stamp on the game's box "This Is PC Gaming" for me back then, because prior to seeing DOOM the only concept of "PC gaming" I had in mind from experience was Chess.
Talk about paradigm change, DOOM did that for me. Well, Ultimate DOOM, that is, since I never really knew Shareware DOOM even existed until quite later. If it had not been for DOOM then I think Duke Nukem 3D would have done it (I.E. brought PC gaming to my attention).
º Command & Conquer: Red Alert
I saw (did not actually play it at the time) the original C&C at my local store's PC demonstration stand, but I ended up buying C&C Gold for my PlayStation, which was in late 1995 if memory is right. When I first saw C&C I knew I wanted to buy a PC "for it", basically as much as I wanted a PC for DOOM at the time. I had no money for that back then so I bought it for the PS1 as soon as it was released. I really enjoyed C&C Gold and because of that purchase my interest for the C&C franchise grew tenfold.
When I first saw and played the original Red Alert (on PC, at my store) for the first time, however, I knew then that I absolutely "had to" get a PC one day. I had been thinking about "gaming on PC" for about two years or so by then, but I never really started thinking about PCs as a real gaming platform until Red Alert got in the portrait. The unfortunate part of that story is that I did end up buying C&C Red Alert (Retaliation) for my PS1, and I consider it unfortunate simply because I never really got to play Red Alert during its real glory days on an actual PC at home.
But at least Red Alert made me "understand the significance" of PC as an actual video games platform that is just as viable and fun as consoles could be... and even better sometimes (DOOM helped introduce that idea in my mind, but Red Alert set it in stone and made it clear). Additionally, the "interests boost" that Red Alert provoked convinced me to "keep track" of new PC games releases, which is when I started looking for PC gaming-related magazines. And from that point even thought I still did not own an actual PC I started to follow news in relation to PC gaming much more frequently than I used to.
º Diablo II
Well, specifically Diablo II (vanilla). We're in summer of 2001, I just got my first PC which happens to be able to play some games, one of which is Diablo II. At the time I had been buying gaming magazines showing PC games (had been doing that for a year already even before buying an actual PC to play PC games with) since I was just hyped about many of them. A year before getting my PC I was already losing some interest in my console games and I couldn't stop thinking about "the day I'd start playing games on my own PC at home".
The original Diablo had been shown and spoken of in some of the magazines I bought and I thought it looked interesting. The irony, however, is that I did end up playing Diablo, but only a year after buying Diablo II. If I recall correctly Diablo II's advertisements (and preview, or review, not sure) in one specific issue of one of those magazines I bought (can't recall the name, maybe it was PC Gamer but I'm not sure anymore) basically "sold it" for me. All I had to do next was to save money from my first full time summer job (when prior to that I had only been doing simply, short-lasting partial jobs in both summers of 1999 and 2000) and wait until I could buy myself a PC and Diablo II.
I did just that, in summer of 2001, and from that point I really "became a PC gamer". I also ended up buying C&C Red Alert, C&C 2 (Tiberian Sun) and SWAT 3 during the weeks that would follow my Diablo II purchase. Due to my job and regular income I ended up buying more PC games in something like four or five months than I ever thought being possible even for consoles. Realizing I was "free to buy which games I wanted" was also an all new concept and experience of its own during that time.
º Half-Life 2
The original Half-Life for PC was released back in 1998. At the time my only experience with FPS games on the PC was DOOM and Duke Nukem 3D from short glimpses and short payed-for play time trials at my local store. My "real" FPS experience back then was Goldeneye 007 and Turok on my N64.
Not to mention that when Half-Life was revolutionizing the FPS genera along with most of the PC industry (for new graphics and engine standards) I myself only heard but short stories of that event when I just happened to read PC gaming magazines at a library (and rarely bought them, I usually just got in the library, briefly looked at some pages fast and got glimpses of "what was happening in the PC gaming world"). So at the time when Half-Life was the new star I was instead immersed in Turok 2 which I had just bought (in December 1998, which I still recall very clearly to this day, and I bought it at a Toys 'R Us).
With this said though, as the months and years passed and as I got to read more and more from PC gaming magazines, that one game that I seemed to have "missed" came back over and over. The impact at the time must have been tremendous, perhaps as big as DOOM itself had done in 1993, because I kid you not when I'm saying I still recall magazines regularly presenting, reviewing (or "re-reviewing", or "re-analyzing") and basically praising Half-Life for a good two years following its release, almost as if it was still new. Well I missed that "PC gaming storm" when it was live, but I sure kept hearing about it and since I didn't know what the "fuss was all about" all I could do was to be curious about it.
For me, the importance of Half-Life and how actually good, awesome and just damn brilliant of a game it was only came to light when I ended up buying the PlayStation 2 version, which came with the exclusive-to-PS2 (at the time) Decay campaign. I remember part of the discussion I had that day with the store clerk. I was there to buy Metal Gear Solid 2 which I had pre-ordered. I had some more money in my pockets and asked him what games might be good that I might have missed. He said something like "well there's this one, Half-Life, but you probably played it already". That's when I suddenly had this memory flash and my eyes got wide open, and then I asked him "oh that's the famous Half-Life from a few years ago on PC yeah?". I think that at that point he kind of realized that I had never played it. He then replied something along the lines of "you... never played Half-Life?". Well, let's just say that I ended up buying it.
So yes I've known about Half-Life from its PS2 version, but I have to add this series and specifically mention the original in this list since even though I was "late to the PC-related Half-Life storm" and its significance I later fully understood all of it. It was indeed a great game and I did end up buying the Half-Life Platinum Collection for my PC some time later, which also allowed me to experience Opposing Force, Blue Shift, the original Counter-Strike and Team Fortress as brand new games (to me).
Now I specifically mentioned Half-Life 2 in bold, that's because, finally, in 2004 I was "fully" PC gamer at the time and once more Valve revolutionized to quite a comparable degree the PC gaming industry with the arrival of its Source engine and Half-Life 2. Finally, live and within the storm I could experience on my own "how it was like" to live through revolutionizing moments, when history-in-the-making was occurring and being part of the crowd experiencing it as an actual PC gamer. Specifically and additionally Half-Life 2 was also the first PC game that brought "PC upgrades" and "new gaming rig" in the bigger picture of PC gaming for me. From summer 2001 to Half-Life 2's first E3 presentations I was still gaming on my same "old" PC. It was only after I saw Half-Life 2 that I really started to learn how to upgrade my own rig and "be prepared" in advance.
I owe Half-Life 2 that much and I also owe it and Valve my first real experience of a live witness of how it feels and looks like when things change on the PC gaming world. I had lived through similar moments with console gaming from late 1989 to around 2000, but it was a first specifically for me when it came to PC gaming, and I'm going to remember it for as long as I can. But I also owe the origin of it all to Half-Life, the first, and the first engine that brought Team Fortress as my first real PC multi-player experience (besides DOOM II in LAN mode). And I and countless others in the PC gaming community owe the original Half-Life engine (gold source) hundreds upon hundreds of modifications, one of them being Natural Selection which is also the first PC game titled as a "mod", being free, that I had just as much fun with (if not more) than "actual brand new sold PC games at the store". That also brought "free and good modded PC games" to my attention.
It just seems to me like I can never praise Valve enough for what they've done for PC gaming at the time, and still today with Steam. So they definitely deserve their place on my own Mount Rushmore of PC gaming.
Conclusion
I could of course name other very influential PC games and series, but really these four mentioned above are the ones that I simply cannot silence.