At least a douple of dozen. But it is tricky, because some warnings may be displayed as words on a computer screen (EICAS - engine indicating and crew-alert system) with one master alert sound meaning "look at the EICAS screen - you have a problem!". And some audible alerts are more advisory than warning - altitude capture; altitude call-outs in feet in the last moments of landing.
And they vary somewhat by aircraft age and type.
Discrete warning alarms with distinct sounds (and I'm sure I'll miss some): master warning, autopilot disconnect, stall warning (horn, beeps, verbal "Stall!, Stall!"), stick-shaker "rattle", "Wind Shear!," overspeed, take-off configuration, "sink rate/Don't sink!," engine fire bells, ground proximity ("Terrain! Pull UP!"), excessive rate of descent ("Pull UP!"), traffic (TCAS) alerts, TCAS resolution advisories ("Climb! Climb!/Descend! Descend!"), bank angle, landing gear not down, (what I can think of off the top of my head).