I know he's not renowned as a singer, but his album of about 10 years ago, Ten Easy Pieces, is a delight. Just him at the piano with his own takes on Galveston, By The Time I Get To Phoenix, Wichita Lineman, The Worst That Could Happen etc.

If you want other people singing his songs, I found an excellent compilation as a Christmas present, it was only a fiver. There must be loads.

Ten Easy Pieces is great. But for a compilation of his best stuff from his solo albums - the originals not remakes - you want "Archive" (WEA 1993).
His voice isn't to everyone taste and most people prefer his songs as done by other people. For this you want "And Someone Left The Cake Out In The Rain" which has all the obvious ones - the Glen Campbell stuff, both the Richard Harris and Donna Summer versions of Macarthur Park, Do What You Gotta Do by the Four Tops, Magic Garden by Dusty, Judy Collins, Scott Walker etc. etc. It came out about ten years ago on Debtante Deluxe, a Polygram label.
Both are highly recommend. Presumably available somewhere.
Webby‘s one of the greats. And if you're new to his music you're in for a treat.

Update: just checked on Amazon and that Tunesmith one looks good too. Try Archive before any of the solo albums - it's the best of them. The Glen Campbell Reunion album wasn't particularly successful, but it's really good.

Archive is very good, best place to start. Mark Ellen wrote the sleeve notes to "And Someone Left The Cake Out..." so it MUST be good. 'Reunion' is well worth checking out as well.