I'd just like to say, these are by no means my favorite games to play, just the games I think helped touhou along the most.
1) Imperishable Night
This was what EoSD and PCB were leading up to; this is what ZUN had been planning since the start of the windows series. While it didn't introduce many new characters, it took a ton of the old ones and expanded on their stories and personalities. Without this game, Remilia would be a Dracula clone instead of a strange little girl. Yuyuko would just be a suicide ghost girl instead of the eccentric-yet-wise food lover we know. We wouldn't have Mari/Ali interactions. Nothing like this would come in a main game until SA, and even then it wasn't done as comprehensively.
2) Embodiment of Scarlet Devil.
In PC-98, ZUN hadn't developed a real canon yet. EoSD was the first time ZUN began to world build instead of just throw in random enemies. In other words, EoSD is where ZUN really began to think about Gensokyo. In addition,it brought us the fan favorites of Cirno, Meiling, Patchouli, Sakuya, Remilia, and Flandre (sorry Rumia =P). However, while it brought a lot to the table, a lot was also swept away in PCB and IN. Most of EoSD's story was retconned in later games, and EoSD's characters didn't really get any personality until IaMP, IN, PoFV, and Hisoutensoku.
3) Mountain of Faith.
This may not be the game that started it all, but it's the game that defines touhou as it is today. Besides the danmaku being less spammy, Mountain of Faith refines ZUN's world building, turning it into a series rather than a cluster of standalone games. After MoF, each game (more or less) connects directly into the next one. However, Mountain of Faith can't really take all the credit like IN or EoSD. It was tthe first link in the chain, but you can't make a chain with only one link.