When the head angle is steeper, the bike becomes more nimble and twitchy. The bike reacts faster to steering input making it prone to oversteer. Road bikes tend to have "steep" head angles in the 72 to 74 degree range. A half degree is more noticeable on bikes with steeper head angles, especially at higher speeds. However, if you're a casual rider than a half-degree probably won't make a difference.
When the head angle is shallower/ slack, the bike becomes smoother and more stable, but prone to understeer. Insofar making half-degree increments almost indiscernible. These angles are commonly associated with mountain bikes and beach cruisers. Slacker angles are sometimes associated with longer wheel bases as well; Boutique bike manufacturers commonly offer 'chopper' style bikes with long wheel bases and super slack head angles. This makes the bike fun to cruise but it's not very nimble.
Mountain bikes tend to have a wider range of head angles available depending on the type of riding you're interested in. XC (Cross Country) tend to be steeper, measuring in the 70 to 71.5 range, and on the other end are DH (Downhill) bikes raking back as much as 64 degrees on popular models. In between those model types are Trail and AM (All Mountain) bikes that have respective head angles.
Another thing to understand is that bikes with rear suspensions have a noticeable affect on the head angle when the rear suspension activates. When the rear suspension squashes, the head angle slackens. It gives the rider more stability while also increasing ride comfort, which is why full-suspension bikes are so popular. There are other benefits but that's another topic :)