Depends on how high you want to go, and how good you are at voltage management. You can usually achieve mild to moderate overclocks if done correctly on stock cooling. Beyond that, after market cooling is a must.
Important thing to consider is also the airflow in the case you're using. The stock cooler may be capable of keeping the CPU cool, but proper ventilation will ensure that the heatsink then dissipates the heat its collecting.
If you do any overclocking, make sure you get some software like CoreTemp that will let you know when you heat gets to unsatisfactory levels
1) What is your ambient temp. This time of year (depends where you live), your room temp is probabaly lower than the middle of summer. My delta is Room = approx 67->68 for winter and around 77 F in summer. For each 1 F rise in ambient temp, cpu temp can rise 1 C. So if you expect a 10 F delta between now and next summer, then you 60 C could easily be 70C.
2) The cooler the better. I have no idea how much say running a CPU 10 degrees hotter has on life expectance other than it will be less.
3) For OCing. When you OC you must run software to verify that your OC is stable. memory/cpu errors can create Havic with your OS, possibly requiring a re-install. Worst case, rare, it can mess up the Bios. Most here run Prime 95 to verify stability. Prime95 will raise your CPU temps MORE than running a game. Stock HSF + prime 95 in many cases results in core temps in the mid to upper 70's, and that is WITHOUT an OC.
.. I'm one that does not recommend taking the stock HSF out of the Box, it is best used as a door stop, or left in the box to prevent it from blowing away - Considering a much better HSF, the Hyper 212 is only around $30 and is MUCH better. That is before appling any OC. I'm a firm believer in running the CPU as cool as cost effective - as I plan on keeping my builds as long as possible. Over a 3 yr period, even an $80 HSF (I have the 9900Max) only works out to 8 bucks a year - LESS than a cup of java per day.
I didnt want to use the stock cooling. I had a antec kuhler h20 920 but it wouldnt fit in my case. So i used the stock cooler. I do plan to get a new cooler so i guess i will just wait to oc till then.