“Surf City,” followed by “Sukiyaki” and “Walk Right In.”
Fingertips-Pt 2 in a walk. Stevie Wonder burst onto the music scene seemingly from nowhere and nailed that mutha. The added plus of Marvin Gaye, who at that time was at the end of his stint as one of The Funk Brothers, makes it even better.
Too close to call. I went with Surf City over Fingertips, but ask me again in an hour and I might go the other way.
Reading these threads reminds me of how low a bar the Beatles had to clear to take the U.S. by storm in 1964.
I went with “Dominique” for 1963 because all the other songs on this list that I remember (all but seven of them, actually) are either fluff or dreck.
But after reading all the comments about “Fingertips” I’m gonna have to give it a listen.
…OK, now I’ve listened to it. And even though (aside from the surprise ending) it’s about 45 seconds of Stevie singing, and 4 minutes of his band jamming, I’m sorry I didn’t vote for that, because quite frankly his band’s jamming knocks practically all of the white pop music from 1963 right off the stage.
Not only would that sort of sound survive the British Invasion, but a lot of “classic rock” has white boys adopting that sort of sound and making it their sound, too. (Classic rock didn’t return the favor: given a better black artist/group original of a song, and a crappier white artist/group cover, you know which one is in the classic rock canon, and which one isn’t.)
“His” band is The Funk Brothers, who were an ensemble of local musicians who wrote and arranged the music for most of the top Motown acts of that era. They were rarely credited by musicians. If you haven’t seen the documentary “Standing in the Shadow of Motown”, I highly recommend it.
Second this. And pair it with “20 Feet from Stardom,” the story of Darlene Love and the other unsung backup singers.
“It’s My Party” is a lot of things but it’s not fluff or dreck.
I voted for Our Day Will Come. There are a few other decent songs here, but overall it’s a weak crop again.
I’m surprised that “Be My Baby” didn’t make it to #1 - it would have gotten my vote. Oh well…
Sorry, not a big fan of “Fingertips”. I should vote for that because of Stevie Wonder, etc, but then perhaps I should vote for “He’s So Fine” because of George Harrison, etc. 
Which is what I did. Again, I really think BMB is the best pop song from the year, but obviously not the best #1.
1964 won’t be too hard for me, but after that it gets pretty impossible. I have half a mind to disqualify myself from voting for the Beatles just so I can make more interesting choices.
Surf City, although I also love “If You Wanna be Happy”.
It is weird that “Be My Baby” was kept off the #1 slot by “Sugar Shack” of all things. I’ll take the Chiffons from this list.
“Sukiyaki” is one of the very few foreign-language songs ever to hit #1 (the word “sukiyaki” is not in the lyrics btw). “Dominique” is another… which happened to be #1 at the moment of the JFK assassination.
According to Wikipedia, the song previous to “Dominique”, “That’s Why I’m Leaving It Up to You”, was #1 on the day of the assassination. That being said, I can understand why The Singing Nun’s song hit #1 shortly thereafter. People were looking some sort of spiritual solace.
Also, in case no one’s noticed it, 1963 is the first year since 1955 when there weren’t any #1 hits by Elvis. I realize this analysis is hindsight from 50 years but I think that indicates there was a vacuum in American popular music and that vacuum was waiting to be filled the following year.
In case anyone’s interested, here is the original 1929 version of Walk Right In by Cannon’s Jug Stompers.
Hard to choose between “He’s So Fine” and “It’s My Party”. I chose the latter because I’ve always liked it since that cover version in the 1980s, and the original is not too different. The Chiffons song is great but for me it has been trumped by “My Sweet Lord”, which is a better arrangement, unconscious plagiarism or not.
If going by the date of the Billboard issue, it was neither. “I’m Leaving It Up to You” was first listed as #1 in the issue dated the day after the assassination, making “Deep Purple” the #1 on the actual day. (But was the issue date the same as the publication date?)
This doesn’t necessarily answer your question, but according to Joel Whitburn, Billboard identified its Hot 100 chart with the designation “week ending [date]” until January 13, 1962. This date differed from the issue date.
From that point forward, the chart date and issue date were the same. One assumes the issue date corresponded with the publication date, but we can’t be sure of that. Many magazines (though perhaps more commonly monthlies rather than weeklies) would have an issue date a month or more ahead of when they actually appeared on the newsstand.
I also have a fond place in my heart for that Japanese song known to Americans as “Sukiyaki”—which is hilarious because its real title is “Ue o Muite Arukō,” meaning ‘I turn my face upwards while I’m walking’; it has nothing to do with any culinary dishes. I like to play it on the guitar and sing it in Japanese, just because. If it hadn’t been for Stevie Wonder bursting onto the music scene with “Fingertips” that year, I might have voted for Kyū (4 Q?).
I’m going with “It’s My Party,” though I’m really not sure why.
I’m gonna back the Four Seasons until they drop off the charts for good.