There isn't much need for a post like this. Enter "ukulele songbook" in Google (without quotation marks) and you'll get so many songs that there's a real danger of being swamped by them. You run the risk of spending more time managing the songbooks than playing their songs! That said, there are three sites worth investigating. If you start with these, it may be unnecessary to go anywhere else!
- Dr. Uke has over 1,500 songs in PDF files. It also has baritone ukulele versions. The site has been archived at archive.org, so the content will continue to be available should the link stop working.
- Richard G has over 1,200 songs in PDF files. The site has been archived at archive.org, so the content will continue to be available should the link stop working.
- A trip to Jim's Ukulele Songbook will get you a songbook containing over 1,200 songs. The songs on Dr Uke and Richard G's sites are intended to be downloaded one at a time. Jim's songbook is a single file containing all of Jim's songs. This songbook, too, has been archived.
As with online songbooks, there's really no reason why one needs a ukulele version UNLESS one wants ukulele chord diagrams accompanying the tunes. Many ukulele songbooks--way too many--are nothing more than guitar songbooks with guitar chord diagrams replaced by ukulele chord diagrams. I'm of two minds about this. OT1H, why not? The buyer gets the songs and the diagrams that make the songs easier to play. OTOH, see note 1.b. (The ukulele is NOT like the first four strings of a guitar capoed at the fifth fret!). One would hope that a publisher would have the courtesy to make the arrangements sound a bit more ukulele-like.
There seems to be--you'll forgive me my observation--considerable price gouging going on. There are too many songbooks where the cost per song seems exorbitant, especially when all that is done is replacing guitar chord diagrams with ukulele chord diagrams. Using current Amazon prices and not naming names, many songbooks come it at about 33 cents per song. Two notable exceptions are The Daily Ukulele and The Daily Ukulele Leap Year Edition, which cost out at a bit less than 14 cents per song.