As has been said here, the "normal" spin entry, and spin itself are relatively gentle maneuvers around 1G. Certainly, there are ways to enter a spin (like a snap roll) where local forces on parts of the aircraft cold exceed the "average" G load on the aircraft. This would be a reason that some Utility category aircraft can be approved for spins, but not aerobatic maneuvers.
It can be the recovery from a spin (or other upset type maneuvers) which can get you in trouble. Extreme nose down attitudes can cause a speed buildup very quickly, and immediate pilot action is vital. I can tell you that a wingover in a Cessna 182RG can result in an alarming speed buildup.
During certification testing, I was required to spin a Cessna Grand Caravan, with an external load. I did a lot of inquiring about spinning such an aircraft before hand. The aircraft was equipped with an accelerometer. I did 14 spins at the extremes of C of G, and at differing weights. The varied C of G produced dramatically different recovery characteristics. Forward C of G consistantly resulted in an extreme dive. Several of the recoveries were very close to Vne, and at 2.8G.
You tube clip of one of the spins I did here: