These are the sound effects that I've harvested so far:

Sound made by the Guardian in 2300
The balloons from the beginning
Magus' bats
Norstein Bekkler's laugh
Azala's Black Tyrano
The pendant breaking
Crono's cat
A noise made by a computer
Crono's confuse technique
Crono drawing his sword
The cure spell
The Deltastorm spell
"Destruction rains down from the heavens"
A door opening (I think)
The Epoch takes off
Lucca's fire spell
Frog's ribbit
Frog drawing his sword
Heckran's scream
Marle's ice spell
Lavos' beating heart
Lavos' scream
Rustling leaves
Leene's bell
Crono's lightning spell
Magus' chanting
Lucca's megabomb technique
A monster sound
Another monster sound
Another monster sound
Another computer type sound
Open a treasure chest
Organ music
Ozzie's laugh
Robo bangs his chest
Robo makes some noise
Earthquake
Save point
The seagulls from the beginning
A type of shadow spell
An electric shock
The start of the game
Computer static
A step forward (or maybe backward)
A strike
Flowing through time
Opening a timegate
A monotonous typing sound
That high-pitched annoying warp sound
Dripping water
Water spell, courtesy of Frog
WRONG