Hopefully this topic will also help others complete their collection, and once the list is completed, I'll start a "Rate each Neil Finn song out of 5" topic in the forum (poll style, so I want to actually include EVERY song).
So please, if I've missed something, anything (apart from any kind of covers), please let me know! Oh... and the dates below are only rough.

1979
From the Frenzy album - give it a whirl.
And from Luton / Frenzy (A&M) - holy smoke
1980
From the True Colours album:
i got you
missing person
what's the matter with you
And the stand-alone single - things
1981
From the Corroboree album:
one step ahead
history never repeats
iris
ships
1982
From Time And Tide:
hello sandy allen
log cabin fever
take a walk
giant heartbeat
1983
From Conflicting Emotions:
bullet brain & cactus head.
message to my girl
the devil you know
strait old line
no mischeif
our day
And the b-side - kia kaha
1984
See Ya' Round:
one mouth is fed
breakin' my back
years go by
doctor love
i walk away
voices
And the 2 i walk away demos - love and success and your inspiration.
And we can't forget serge - also recorded in those sessions (?).
1986
From the first Crowded House album, there were 9 songs (10 if you count i walk away II) + can't carry on (on some versions of the album).
And of course there was recurring dream.
1988
10 songs from Temple Of Low Men.
Plus lester.
1991
13 Neil / Neil-Tim songs from Woodface.
Plus:
anyone can tell
dr livingstone
i love you dawn
i can't stand it (never released though

left hand
sacred cow
thirty-three years
convent girls
the same language as me
time immemorial
strangeness and charm
tail of a comet
prodigal son
my legs are gone
in love with it all
the same language as me
newcastle jam
^ ^ ^ WOW! Forget a double album... Neil should have released a triple album back in 1991!

1993
12 songs from Together Alone.
Plus:
i am in love
you can touch
zen roxy
Neil Finn also recorded a duet with Yothu Yindi, titled dots on the shells, written by Neil & their lead singer.
And help is coming, recorded a little bit later.
1995
11 songs from The Green Album
1996
3 new songs from Recurring Dream:
everything is good for you
instinct
not the girl you think you are
And mary of the south seas - a Neil & Tim song recorded for the Common Ground compilation.
And hamburg jam - a song recorded live in 1996 by CH.
1998
13 songs from Try Whistling This.
Plus the b-sides:
808 song
family ties
identical twin
log drums
she comes scattered
tokyo
And the single can you hear us?.
And the "unreleased" spirit of the stairs.
2001
The 10 songs that made both One Nil and One All.
Plus the 2 songs not included on One All - don't ask why and elastic heart.
And the One Nil b-sides - underestimated and now i get it.
The live recording of edible flowers from the 7 Worlds Collide album.
The One All inclusions - lullaby requiem and human kindness
Also, sweet secret peace - a song released on a compilation in 2002.
The 5 Neil vocal tracks from the Rain soundtrack:
summer of love
you don't know
orange and blue
boat joyride
drive home
And the 7 other Neil-penned instrumentals from the Rain soundtrack (I won't name them all).
Neil also did a duet with Deborah Conway, which was released on the 2002 Deborah Conway Best Of album. The song was called exquisite stereo, but I haven't heard it, don't know where to find it, and don't know if he co-wrote it or not. Help is appreciated here!
There was the Neil & Tim demo of the land and the sea.
Other songs performed live during this period - love is all that remains and gentle hum are all that spring to mind, but i'm sure there's more.
UNKNOWN ERA
forever friends
frank's dark past
be my guest
most unwanted
snake charm boogie
my old friends (cover?)
please release me (cover?)
preparations (cover?)
burgler's song (written by Neil & Liam)
+ more, but we'll start with just those.
[ / END MASSIVE LIST! ]
Woah! Phew!

Now you're job is to let me know which obvious / obscure songs I've left out of Neil's career!
Please don't let this thread die... it took me ages to write this out!

Thank you all in advance.