EDIT TO ADD INFORMATION REQUESTED.
If a helicopter is flying low, and not "squawking", there is no way that any civilian radar will pick it up. Especially in a mountainous region such as Pakistan. Simple mechanics of radar as illustrated by this picture from Answers.com. Note that mountains between the radar site and aircraft will further block the ability of the radar to detect an aircraft.
Keep in mind that if they can't be seen, they can't get shot at either. And these are some of the best helicopter pilots on the planet. Most radars are unable to detect anything flying contours, but I would wager that for part of this they were flying nap of the earth. The below image is taken from the Global Security Website (the exact image is from Figure 28 on this page) where they discuss many modes of flight for helicopter safety from enemy fire.
Even larger aircraft like the FB-111 would use this technique to avoid detection without the need for stealth technology.
So even though the airspace is monitored, if they can't be seen, it doesn't matter. Also, I don't think this was "allowed" or "disallowed" by the Pakistani government. Some covert operations are carried out, and then back-briefed if the target (such as Osama bin Laden) is important enough.
Now, several folks have asked about the helicopters used, and some of their performance characteristics. The most likely aircraft (as reported in a couple of other answers as well) is the MH-60 Pave Hawk (a Blackhawk variant modified for special operations). Again, to quote Global Security, the performance characteristics are:
Primary Function Infiltration, exfiltration and resupply of special operations forces in day, night or marginal weather conditions.
Power Plant Two General Electric T700-GE-01C engines
Thrust 1,630 shaft horsepower, each engine
Length 64 feet, 8 inches (17.1 meters)
Height 16 feet, 8 inches (4.4 meters)
Rotary Diameter 53 feet, 7 inches (14.1 meters)
Speed 184 mph (294.4 kph)
Maximum Takeoff Weight 22,000 pounds (9,900 kilograms)
Range 445 nautical miles; 504 statute miles (unlimited with air refueling)
Armament Two 7.62mm mini-guns
Crew Two pilots, one flight engineer and one gunner
In particular, note that these aircraft are mid-air refulable from a KC-130 (NOT KC-135), thus they have a nearly unlimited range. I highly doubt that they took off from anywhere inside Pakistan (i.e. Ghazi) but rather originated in Afghanistan. I cannot say where exactly though, but no matter where they took off from, if they received refueling prior to entering Pakistan, the range is more than adequate to get to Abbottabad and back on one tank of gas (looking at google maps, it appears that the distance is less than 350 KM from Kabul, or about 200 miles). So a little less than 400 mile round trip, at about 200 MPH would be about 2 hours total (add in the actual assault and there you have your timeline). These figures are approximate though because things change with load-out and other configurations. These aircraft would probably have flown in a formation that would probably helped to disguise their true numbers.
Someone mentioned that ATC must have a squawk to paint these aircraft. That is overstated, however as previously mentioned, they were probably well below the radar, and aided by the mountainous terrain. Add in they were most likely using EMCON 4 procedures, and then it would be even more difficult to pick them up by any means. As the cited article also mentioned, the noise reduction and additional radar absorbent paint just added to the stealthiness of these aircraft (as if SPEC OPS flight patterns were not enough).
And thanks to Kit Sunde, we have further info: Here's Pakistan denying having known about the raid, "Bin Laden: Pakistan intelligence agency admits failures", BBC which also states: "US helicopters entered Pakistani airspace making use of blind spots in the radar coverage due to hilly terrain."
Feel free to leave more questions if you have them.