Extremely important. You want to make sure you apply it correctly, too, using a clean flat-surface object much like the credit-card shaped object that comes with some thermal paste tubes. Spread it on with that, making sure that all previous paste is thoroughly cleaned off with some sort rubbing alcohol and Q-tips.A very thin layer is best, enough to just cover the entire metal surface on top of the die. Smooth it out, too. Fingerprints and unevenly spread glue can create an improper bond between the heatsink and the die. Make sure the bottom of the heatsink is clean, too.
Lastly, if you want to trade easiness for efficiency, good thermal paste like Arctic Silver brand paste will maximize the heat dissipation between the die and the heatsink.