Is there a limit to the number of parallel LED if each has its own resistor?
Basically no, there isn't a theoretical limit. Though there are some practical ones:


How lossy your power supply cables are - the associated resistance will cause a voltage drop proportional to the current. The more branches you chain off the supply cable, the higher the current, and so the more the voltage drops.
How much power the supply can provide - if you try and drive a million LEDs from a 1A supply, clearly things aren't going to go well.
Your wallet - for example a million LEDs would cost a fair amount. But then I suppose you are unlikely to go for that many :)
Time - wiring them all up takes a fair bit
Thermal considerations - stick a large number of LEDs and resistors in a small space with inadequate consideration for the amount of power being dissipated, and the whole thing will heat up until something gives in.