Harnesses / Helmets
Climbing harnesses are probably the most important of all safety equipment. The belay loop is just a small band of (heavily reinforced!) material but it's always a crucial component in the rope system, and the fit and style of harness will go a long way towards determining how comfortable you are when on belay for long periods, how you sit when rappelling or on a hanging belay, and how clean and painless your falls are. Nobody who has taken a fall in an old-fashioned, early model sit harness ever wants to let go of their lightweight, modern, comfortable one. A climbing harness is usually the second piece of gear a novice climber buys and there might be no need to worry about upgrading for years to come. It takes far longer for a harness to wear out than a pair of shoes, which may go at the toes within a season or two if you climb frequently. But that doesn't mean you shouldn't change your harness every two or three years at least. Like all soft goods they will weaken over time. If yours looks battered and the belay loop is fluffy it's time to invest in a new one.
Some climbers don't wear helmets, but this category is largely populated by indoor climbers and maybe a few sports climbers. If you're going to climb without bolts you definitely need a helmet to protect against rocks and fall injuries, and helmets are also strongly recommended for sports climbing, especially if you plan to push your grades. They're absolutely essential for ice routes. Modern climbing helmets are strong, adjustable, and lightweight - the Petzl Meteor III and Black Diamond Tracer come in at just over 230g each. They won't interfere with your climbing and might just save your life.