Lead vocal: John, Paul & George [John on bridge]
If you look at the B-Sides on the singles before "I Want to Hold Your Hand", you notice (as I noted in their entries) that they are all harmony exercises."This Boy" is the last B-Side like this, until "Yes It Is" nearly two years later.
"This Boy" is, without a doubt, the best of them. It shows the boys taking that girl-group formula and putting it to use on their own song. Whereas "I'll Get You" was more or less John and Paul singing lead at the same time, "This Boy" features them actually using the harmonies. A great example is during the bridge, where John takes lead ("Oh and this boy, would be happy...." is probably one of John's best vocal moments) and Paul and George sing back-up, just like the bridges in the girl-group songs that influenced them so much. Then you have Ringo doing his perfect percussive shuffle behind them.
As a side note, "This Boy" got some funny attention when it was used in A Hard Day's Night as "Ringo's Theme" (of which the soundtrack recording was issued as a George Martin single in the US that actually charted!). In the US, "This Boy" was just an album track on Meet The Beatles! as Capitol used the much more upbeat "I Saw Her Standing There" as the B-Side to "I Want To Hold Your Hand".