Tusk
Hypnotized
the Chain
Oh, Well
Dreams

Songbird
Rhiannon
Tusk
Dreams
Go Your Own Way
The Chain
Tell Me Lies
Landslide
Silver Springs
Don't Stop

Of course!

1. Landslide
2. Everywhere
3. Rhiannon
4. Dreams
5. Don't Stop

Black Magic Woman (they wrote it, and did it 1st)
Green Manalishi
Rattlesnake Shake
Oh Well
Madison Blues
Albatross

5 it's not enough so I'll give you 10:

1) Gipsy
2) Landslide
3) Dreams
4) Little lies
5) Hold me
6) You make loving fun
7) Sarah
Don't stop
9) Go your own way
10) Everywhere ☺

My top 10 Fleetwood Mac songs would be from their earlier days, prior to the enormous commercial success of the band. They did achieve moderate success during the late 60's-early 70's in the UK and Stateside, but nowhere near the scale of Rumours etc, by the mid 70's and onward. I've always preferred the bands earlier material.:

1) Watch Out
2) Black Magic Woman
3)One Sunny Day
4) The Green Manalishi (With the Two-Prong Crown)
5) Station Man
6) Oh Well
7) Rattlesnake Shake
Fleetwood Mac
9) Future Games
10) Long Grey Mare

Here's a few videos...

Rattlesnake Shake:
http://www.youtube.com/watch?v=TqKKGDcexZs
Oh Well:
http://www.youtube.com/watch?v=KE4HGlmtOcg&feature=related
Dust My Broom:
http://www.youtube.com/watch?v=_fcHm36PR7k&feature=related
Albatross:
http://www.youtube.com/watch?v=bSZHT2XvoLM&feature=related
Like it This Way:
http://www.youtube.com/watch?v=HQ8AcEYTEFY&feature=related
World Keep On Turning:
http://www.youtube.com/watch?v=rxux5LdmjQU
Homework:
http://www.youtube.com/watch?v=_QmxYKNkdno&feature=related

Perhaps if this was my top 50 list, then maybe a few Buckingham/Nicks era Fleetwood Mac tunes might sneak in there. I do like some of that stuff, but not on the same level as the Peter Green, Jeremy Spencer, Danny Kirwin, or even Bob Welch era for that matter. I thought I would limit my list to 10 songs by this excellent group, as you've indicated in your query.
Fleetwood Mac had released around 14 albums in the 6 years as a band prior to Buckingham/Nicks joining the ranks. That era has a much better variety of music to chose from in my opinion. Despite what Billboard Magazine might tell us.
Worth looking into, if you haven't already.

meh.. take em or leave em here.... Rhiannon is good.. as is the chain.

My Top 10 of Fleetwood Mac

1 Hold Me
2 Sands Of Time
3 The Green Manalishi (With The Two Pronged Crown)
4 Station Man
5 The Ghost
6 Tusk
7 Never Going Back Again
8 Hypnotized
9 Silver Springs
10 I Don't Wanna Know

You called?!
James, I *LOVE* Fleetwood Mac! The 'longest-serving' of my 5 equal favourite bands

Now, I know I've already posted this answer on another question, but it's pretty hard for me to narrow-down my favourites, and this is my current list :~


Peter Green era :~
Dragonfly
Underway {full 16+ mins version}
Black Magic Woman
Shake Your Money Maker
Albatross
Oh Well {parts 1 & 2}
The Green Manalishi
Need Your Love So Bad

1970 - 1975 {thus far ~ only just filling-in this era gap} :~
Why
Station Man
Trinity
Hypnotised

Post-1975 : Buckingham Nicks era {roughly chronological} :~
Rhiannon
Say You Love Me
I'm So Afraid
Second Hand News
Dreams
Silver Springs {full 6+ mins 'outtake' version}
The Chain
Songbird
Go Your Own Way
You Make Loving Fun
Gold Dust Woman
{basically, the entire "Rumours" album!}
Sisters of the Moon {'single' version}
Tusk
Angel
Brown Eyes
Storms
Beautiful Child
Gypsy
Isn't It Midnight
Big Love
When I See You Again
Come
Running Through the Garden


********* ********* ********* ********* ********* *********
Patrick :
I knew I couldn't let you miss this one!

Tusk
Hypnotized
Gold Dust Woman
Oh Well
Rhiannon
The Chain
Silver Springs
You Make Loving Fun
Moday Morning
Don't Stop
Go Your Own Way
Songbird
Black Magic Woman
Green Manalishi