I re-watched Game 5 of the Finals the other night. Got chills towards the end when Pop was taking the big 3 out one by one and they'd hug everyone on the sidelines.
Not gonna lie, that Game 6 against OKC had my blood pressure going through the roof. I was watching it with friends and I was having to try so hard not to have a complete meltdown and look like an idiot

Pretty sure I said "We're really going to ing choke this series away aren't we?!" at least 3 or 4 times. Then when Ibaka got away with goaltending I started throwing a damn temper tantrum lmao.
As for other games, Game 7 against Dallas was nice and as others have said, that was when we really kicked it up into postseason form IMO. Game 5 against Portland was pretty good; I remember Kawhi went off in that game. Game 4 against Dallas was when Manu went stupid (in a good way) and I believe when Splitter of all people carried us in the 4th
I was there live for Games 1 and 2 against OKC and while I haven't watched them again yet, I remember them being insanely fun...but a lot of that probably has to do with the fact I was drunk as and watching it live.