Grips can be easily changed to customise your bike or if you have worn your existing grips out. A common purchase for those newer to cycling is to opt for a more comfortable 'dual compound' design where softer rubbers are mixed with harder rubbers to create a more comfortable design. There are also grips available that are paddle shaped to give you are larger surface area for your palm to rest upon.
Mountain bikers have a preference towards the popular 'lock on' type grips, which can be easily fitted and secured in place firmly with small allen key bolts. This stops the grips from rotating when they get wet making the bike safer. The most popular brand for lock on grips is ODI. For a long time, this brand actually made lock on grips for most of the other brands. Colours and grip patterns vary as too does tackiness of the grip. Some can be very firm and others soft and sticky for the ultimate grip.
BMX bikes and scooters use slightly longer grips, this allows room to move on the handlebars when you are doing tricks or stunts. The grips generally have a flange to protect the riders hand from slipping onto the brake levers or across the handlebar.
Bike handlebar grips will also fit on stunt scooters.