very incomplete list, because there's so much great Finn stuff around (ie. I don't know all of it and it would be troublesome to list all of my favourites), but here are a few good ones.
Split Enz songs
This was Neil's first group - they were sort of a funky new wave act, not sure whether you'll like them too much.
History Never Repeats
I See Red
I Got You
Message To My Girl
Crowded House songs
Neil's most famous band. Melodic pop of the highest order.
Don't Dream It's Over (the big hit, one that I really can't listen to for very often these days unless it's live or acoustic or something)
Four Seasons In One Day
Into Temptation
Fall At Your Feet
Whispers and Moans
Better Be Home Soon
I Love You Dawn
Together Alone
Private Universe
Finn Brothers
Neil and his brother Tim recorded one or two albums under this name, I think. The song 'Angel's Heap' is the only one I'm familiar with.
Neil Finn solo songs after the break-up of Crowded House are fairly good too.
Into The Sunset
Driving Me Mad
She Will Have Her Way
Lullaby Requiem
Turn and Run
Human Kindness
Last To Know
Love This Life
In addition, the man does a great version of the Smiths' 'There Is A Light That Never Goes Out' and Crowded House did a fairly interesting take on 'Anarchy in the UK' once.