LEDs in Parallel, each with its own resistor
Your schematic is not ok, but your description is.

If you are using one LED and then the proper resistor the connection is fine. For instance (led values taken as example):







simulate this circuit &ndash; Schematic created using CircuitLab

Anyway, you will be wasting at least 3/4 of your power on the resistors.

My suggestion, whenever possible, put the maximum amount of leds in series:







simulate this circuit

Just keep in mind that


you should not exceed 9-10V of drop on the leds (so for instance max number of 3V leds is 3)
all the leds in the same line will sense the same current
you will not be able to individually control the leds, just the lines (not a problem if you plan to turn them on
for every branch, you will need to have at least one current-limiting device (a resistor is the cheapest option, but if you want higher quality control you can also use a constant current circuit made by two transistors and two resistors)


Note: as Olin said in the comments, many times you may want different currents for different LEDs. For instance, low brightness red LEDs may need a higher current than the standard blue ones, so it needs some balancing. So putting the leds in series should be the last step; please test the various currents before, in order to choose the appropriate value so that the effect is ok for you, then you can group them by current like shown before.