Besides safety, all types of gear are available to make your ride easier, faster and more enjoyable. Things such as lighter wheels and frames for a faster and easier ride, to gloves and padded pants for a more comfortable ride.
Gear and Accessories
If looking to up ones speed, tires are probably the first place one should look. Reducing weight on the tires reduces the inertia required to move the wheels and has a far greater effect than reducing the same amount of weight from the frame. Mountain bike frames have options for road slick type tires and road bike frames also have options for treaded tires. Both also have crossover options for both road travel and a bit of off-roading.
Pedals are a good second place to look at for improving efficiency. Standard/platform pedals are your normal pedals and are generally the most convenient pedals, no special gear needed. The single drawback is that due to their convenience, they are the leasst effecient pedal. Next up are toe clips, these are similar to platform pedals in ease of use, but also provide surface with which to exert force on the up-stroke as opposed to only pushing on the down-stroke. 'Clipless' pedals, like the ones in the image require special shoes, but allow for force to be exerted on the entire down-stroke and up-stroke of pedaling.
The bike frame, fork and other components are another option for reducing weight and/or easing ones ride. There are as many different styles for frames as there are pedal or wheel styles, all with different benefits and/or trade-offs. Ultimately it's up to the rider to decide on what fits best.
Beyond looking stylish, eyewear has another important function. Eyewear protects the eyes, both from UV rays which can damage ones eyesight, but also from particulate matter which can get into the eyes and possibly cause damage.
Having spare inner tubes is part of preparedness for biking. There's always the risk of running a flat and getting stranded is no fun. Pack one, or two spare inner tubes so you've always got your ticket back home.
Having a way to inflate your spare inner tubes will make them significantly more useful. THere are small compact hand-pumps, or there are also CO2 canisters which can be used. CO2 canisters make inflating spares incredibly fast and easy, but they expend rather quickly, so it's important to control it well.