Whether you have an air rifle for dispatching small game or a large-bore rifle for taking out bears, keeping your riflescope sighted properly is essential. There are several reasons for this, not just the obvious ones of simply being accurate.
First, a good hunter strives to minimize suffering. The point of a shoot is to get a clean kill with minimal bullet expenditure. It's not to cause pain and suffering to an animal. Therefore keeping your rifle sighted ensures that you minimize unnecessary injuries.
Next, consider safety. Hunters need to be able to predict where the shot will land. While this isn't as important with a low-powered rifle, such as an air rifle, it's essential for anything that uses a charge to propel the bullet. A .303 bullet has a killing distance of up to a mile, so if there's nothing to stop the bullet, you don't know where it will land. Keeping your rifle sighted will ensure that you know where that shot will end up every time.
Of course, if you're using the gun to repel a bear or a cougar, that shot needs to be accurate to save your life. If your scope is inaccurate, you may not have time to reload or even pull the bolt again. Bears are remarkably resilient creatures and can need several shots in the head to take them down, and even deer will run up to 100 yards despite a large lump of metal in their lungs. Keeping your rifle sighted keeps you alive.
Cost is a final, albeit minor, consideration. The more bullets you spray into the undergrowth, the less likely your shoot will be successful and the more ammunition you need to buy. When you have rifle bullets that can cost up to a dollar a pop, you need to be conscious of how often you pull that trigger. A miss will also scare off most of the local wildlife, so your shoot will likely be less of a success.
Your scope or sight is but one part of the weapon, but in many ways, it's the most important part. An inaccurate scope means your hunt won't be as successful, which can put a downer on the day. It can also lead to more serious problems if it's wildly out, so keep it sighted at all times.
That means you need to shoot a couple of rounds at a good target before you go out shooting. Ensure you have a screwdriver handy so that you can adjust your scope and make sure that the grouping is close together--usually you need at least three shots in the same place to ensure that your rifle is appropriately sighted up. Once that's done, you have a good chance of hitting your target each and every time.