There are 511.

I made the following spreadsheet, which might be of interest to somebody who wants to track their progress: http://www.thunderpeel2001.com/GameFAQs/MGS2-Missions.xlsx

Top tip: These are some amazing tutorial videos by user "Dat Boi Treezy" for getting past the tougher levels, too: http://bit.ly/VirtuallyImpossible

Here's the complete list I put together:

RAIDEN
VR MISSIONS
Sneaking - Sneaking x 10
Sneaking - Eliminate All x 10
Weapon Mode x 40
First Person View Mode x 5
Variety Mode x 7
ALTERNATIVE MISSIONS
Bomb Disposal Mode x 5
Elimination Mode x 10
Hold-up Mode x 10
Photograph Mode x 6

Raiden Total = 103

RAIDEN (Ninja) (available when Raiden is 50% or higher)
VR MISSIONS
Sneaking - Sneaking x 10
Sneaking - Eliminate All x 10
Weapon Mode x 5
Variety Mode x 1
ALTERNATIVE MISSIONS
Bomb Disposal Mode x 5
Elimination Mode x 10

Raiden (Ninja) Total = 41

X RAIDEN (available when Raiden and Raiden (Ninja) are both 100%)
VR MISSIONS
Streaking Mode x 1

X Raiden Total = 1

SNAKE
VR MISSIONS
Sneaking - Sneaking x 10
Sneaking - Eliminate All x 10
Weapon Mode x 40
First Person View Mode x 5
Variety Mode x 7
ALTERNATIVE MISSIONS
Bomb Disposal Mode x 5
Elimination Mode x 10
Hold-up Mode x 10
Photograph Mode x 7

Snake Total = 104

PLISKIN (available when Snake is 50% or higher)
VR MISSIONS
Sneaking - Sneaking x 10
Sneaking - Eliminate All x 10
Weapon Mode x 40
Variety Mode x 2
ALTERNATIVE MISSIONS
Bomb Disposal Mode x 5
Elimination Mode x 10
Hold-up Mode x 10

Pliskin Total = 87

SNAKE (Tuxedo) (available when Snake and Pliskin are both 100%)
VR MISSIONS
Sneaking - Sneaking x 10
Sneaking - Eliminate All x 10
Weapon Mode x 40
Variety Mode x 2
ALTERNATIVE MISSIONS
Bomb Disposal Mode x 5
Elimination Mode x 10
Hold-up Mode x 10

Snake (Tuxedo) Total = 85

SNAKE (MGS1) (available when Snake (Tuxedo) is 100%)
VR MISSIONS
Sneaking - Sneaking x 10
Sneaking - Eliminate All x 10
Weapon Mode x 40
Variety Mode x 3
ALTERNATIVE MISSIONS
Bomb Disposal Mode x 5
Elimination Mode x 10
Hold-up Mode x 10

Snake (MGS1) Total = 88

Total VR Missions = 358
Total Alternative Missions = 153

Total Missions = 511