Highest Chart positions according to the best resources I have available.
The US numbers are from Billboard. The UK numbers are from the current official chart site.
It should be noted that both countries had multiple charts at the time which could be considered official, for example in the US they used both Billboard and Cashbox as major charts.
Positions from other countries are from the best sources I could find online and so should not be considered definitive.

NEW! You can sort by title, date or country but clicking the header.

Singles

Title Year US UK Australia Germany Others
Reflected 1969          
Shoe Salesman 1970          
I'm Eighteen 1970 21        
Caught In A Dream 1971 94        
Under My Wheels 1971 59 66      
Halo Of Flies 1971         Netherlands: #5
Belgium: #24
Be My Lover 1971 49        
School's Out 1972 7 1 39 5 Austria: #12
Netherlands:  #9
Norway:  #6
Elected 1972 26 4 83 3 Austria: #3
Netherlands:  #5
Belgium: #21
Hello Hurray 1973 35 6 95 13 Austria: #16
Netherlands:  #6
Belgium: #19
No More Mr Nice Guy 1973 25 10   10 Austria: #14
Netherlands:  #6
Belgium: #20
Billion Dollar Babies 1973 57     30  
Teenage Lament '74 1973 48 12 89 43  
Muscle Of Love 1973          
Department Of Youth 1975 67   7    
Only Women Bleed 1975 12   50   New Zealand: #21
Welcome To My Nightmare 1975 45        
I Never Cry 1976 12   23    
(No More) Love At Your Convienience 1977   44 54    
You And Me 1977 9 44 3   New Zealand: #21
How You Gonna See Me Now 1978 12 61 9   Netherlands: #9
Belgium: #5 / weeks: 10
New Zealand: #19
From The Inside 1979          
Clones (We're All) 1980 40   36 58  
Talk, Talk 1980          
You Want It, You Got It 1981     74    
Who Do You Think We Are 1981          
Seven And Seven Is 1982   62      
For Britain Only 1982   66      
I Am The Future 1982          
I Love America 1983          
He's Back (The Man Behind The Mask) 1986 56 61     Sweden:  #4
Teenage Frankenstein 1987   80      
Freedom 1987   50      
Poison 1989 7 2 3 25 Switzerland:  #13
Netherlands:  #8
Belgium:  #22
Sweden:  #10
Norway:  #3
New Zealand:  #2
Canada: #40
House Of Fire 1989 56 65 72   Canada: #98
Bed Of Nails 1989   38 13   Sweden: #18
New Zealand #27
Only My Heart Talkin' 1990 89   47   Canada: #78
Trash 1990          
Hey Stoopid 1991 78 21 32   Netherlands:  #22
Belgium:  #36
Sweden:  #19
Norway:  #5
New Zealand:  #17
Love's A Loaded Gun 1991   38 125    
Burning Out Bed 1991          
Feed My Frankenstein 1992   27 169    
Lost In America 1994   22 65   New Zealand:  #46
It's Me 1994   34 77    
Gimme 2000   85      
Novcaine 2003          
Keepin' Halloween Alive 2005          
I'll Bite Your Face Off 2011          
Paranoiac Personality 2017          
The Sound Of A 2018          

Albums

Title Year US UK Australia Germany Others
Pretties For You 1969 193        
Easy Action 1970          
Love It To Death
Gold (06/11/72)
Plat. (30/07/01)
1971 35 28      
Killer
Gold (28/01/72)
Plat. (13/10/86)
1971 21 27      
School's Out 1972 2 4 5 3 Austria:  #8
Norway:  #5
Billion Dollar Babies
Gold (27/03/73)
Plat. (13/10/86)
1973 1 1 4 9 Austria:  #4
Netherlands: #1
Norway:  #6
Canada: #2
Muscle Of Love
Gold (07/12/73)
1973 10 24 36    
School Days 1973       46 Netherlands:  #8
Greatest Hits
Gold (15/10/74)
Plat. (13/10/86)
1974 8   71    
Welcome To My Nightmare
Gold (30/05/75)
Plat. (14/08/90)
1975 5 19 5   New Zealand:  #24
Goes To Hell
Gold (23/11/76)
1976 27 23 4   Sweden: #47
Lace And Whiskey 1977 42 33 3   Sweden:  #43
New Zealand:  #32
The Alice Cooper Show 1977 131   29    
From The Inside 1978 68 61 12   Netherlands:  #14
New Zealand:  #14
Flush The Fashion 1980 44 56 32   Sweden:  #34
Norway:  #32
New Zealand:  #40
Special Forces 1981 125 96 76    
Zipper Catches Skin 1982          
Da Da 1983   93      
Constrictor 1986 59 41 94   Sweden:  #17
Raise Your Fist And Yell 1969 73 48     Sweden:  #15
Trash
Gold (03/11/89)
Plat. (05/02/90)
1989 20 2 5 16 Austria: #4
Holland: #53
New Zealand: #6
Sweden: #6
Switzerland #10
Norway: #4
Hey Stoopid 1991 47 4 18   Austria: #5
New Zealand: #22
Sweden: #9
Switzerland: #7
Norway: #36
Hungary: #27
The Last Temptation 1994 68 6 15 18 Switzerland: #13
Classicks 1995     133 71  
A Fistful Of Alice 1996   76 71    
Brutal Planet 2000 193 38 213 23 Switzerland: #66
Germany:  #23
Austria:  #49
Sweden:  #31
Dragontown 2001 197 87 182 54 Switzerland:  #98
Germany:  #54
Austria:  #75
France:  #142
Sweden:  #41
The Definitive Alice Cooper 2001 33 66
The Eyes Of Alice Cooper 2003 184 112   78 Germany:  #78
Austria:  #72
Sweden:  #59
Finland:  #40
Dirty Diamonds 2005 169 89   71 Germany:  #71
Austria:  #66
France:  #159
Netherlands:  #88
Sweden:  #40
Along Came A Spider 2008 53 31   26 Switzerland: #37
Canada: #19
Sweden: #25
Netherlands: #76
Norway: #33
Finland: #31
Austria: #37
Denmark: #46
France: #101
Welcome 2 My Nightmare 2011 22 * 16   Canada: #28
Finland: #17
Hollywood Vampires 2015 43 30 34 59 Austria: #62
Belgium: #76/34
Netherlands: #47
France: #54
Switzerland: #24

Paranormal 2017 32 6 4 4 Canada: #17
New Zealand: #33
Finland: #9
Sweden: #6
Netherlands: #24
Norway: #15
France: #57 (#23 on physical sales chart)
A Paranormal Evening At The Olympia 2018 42* 26/64** 49 23
*6 on "tastemakers" chart,10 on "independent albums" chart
**26th on "Sales Chart", 64th on overall chart
France: #91
Switzerland: #48
Austria: #17
Netherlands: #142
Belgium:
#28
Sweden:
#58


 

*Note: 'Welcome 2 My Nightmares' chart positions are confused by the fact the album first came out in the 'Classic Rock Fan Pack' which wasn't eligible for the charts. Most UK and a large number of European and US people got the album this way, so when it was released to retail most fans already had it, obviously effecting sales positions.

Some important facts about album certification status

1) What the public often doesn't realize is that US Platinum albums (sales of over 1 million units) only came into being in 1976! Prior to 1976, there was only gold certification (sales of over 500,000 units). 'Billion Dollar Babies' DID, in fact, sell more than a million copies in 1973, but there was no platinum certification prior to 1976. 'Welcome to My Nightmare' DID, in fact, sell more than a million copies in 1975. In fact, 'Welcome To My Nightmare' sold more than 1,500,000 copies in 1975 but there was no platinum certification prior to 1976. 'Killer' and 'Alive Cooper's Greatest Hits' had also sold over 1 million copies in 1972 and 1974 respectively. So, Alice had at least four albums that had sold over million copies each but they were not certified platinum because they were released prior to 1976.

2) In 1986, Warner Brothers finally got around to retroactively certifying million-selling albums that had done so prior to 1976. So, that's why those above-mentioned albums were finally certified platinum in 1986. Notice that Warner Brothers waited ten years to retroactively do so. So many AC albums did NOT take a long time to sell over a million copies. They just were released prior to 1976! Furthermore, other albums like 'School's Out' sold over a million copies way before 1986 but had to be retroactively certified after 1986 too.
(Susie (Glamprincess), August 2005)