1. Computer: a must have for the majority of cyclists, cycling computers have many functions. Depending on the model, these include:

• Speedometer (current, average and maximum speed)
• Odometer (current trip distance and overall distance)
• Cadence (pedaling frequency, rounds per minute)
• Temperature
• Clock
• GPS
• etc.

If you're on a budget, I recommend the Sigma BC 1609 computer. If you want a high end computer with GPS and maybe a heart rate monitor, take a look at the Garmin Edge computers on Amazon and ChainReactionCycles.

2. Helmet: Protect your head. Need I say more? All helmets are equally safe. More expensive helmets tend to be lighter, better ventilated and have a better fit system.

Budget helmet: Giro Indicator.
High-end road helmet: Giro Aeon.

3. Mirror: There are handlebar mirrors and helmet/sunglasses mounted mirrors. Which kind of mirror is better? Some prefer the former, some like the latter. So it's your choice. If you prefer a helmet mounted mirror, I recommend the Bike Peddler Take A Look mirror, which can also be mounted on your sunglasses.

4. Fenders/mudguards are a must have for touring and commuting. They prevent dirty water (mud, sand, salt, you name it) from being thrown on you and your bike. The front fender also protects the lower part of the headset from dirt that might otherwise destroy it if not serviced regularly. Full length fenders offer better coverage, especially for commuters. Shorter fenders don't protect as well, but are better suited for mountain bikes. Fairly good prices  here and here.

5. A bell is great for warning pedestrians. However, if you want to let motorists know you're there, you'll want an Airzound! That thing is really loud, cheap and refillable with any bike pump.

6. A bike rack is essential for touring. It's also great for commuting, as it allows you to carry a bag with you. If you're like me and can't stand backpacks for prolonged periods of time, a rack + bag are indispensable. I've had the Topeak Super Tourist DX and Topeak MTX TrunkBag DXP for more than a year now, and couldn't be happier.

7. Mini/frame pump. One of the most important bike accessories is a mini pump. A mini pump is just a pump that isn't a floor pump and can be mounted to your bike's frame. I recommend the kind of pumps that have a flexible hose, like Topeak's Road Morph or Turbo Morph. It's a lot easier and faster to pump a tire with a flexible hose pump.

8. Bottle and bottle cage and/or hydration pack. When cycling, you have to stay hydrated. Mounting one or more bottle cages to the frame will allow you to take water bottles with you. Or you can buy a hydration pack like Camelbak, which will allow you to take 1.5, 2 or 3 liters (50, 70 or 100 oz) with you. Hydration packs are more effective at keeping you hydrated, as it's a lot easier to drink from them, even without stopping. Camelbaks are high quality, and really cheap for what they offer.

9. Front lights have two purposes: let you see and be seen. There are powerful lights that do both. You need these if you ride at night with dim or no street lights. Less powerful lights are cheaper but you won't be able to see well in front of you. So they're best suited for city riding, where there's a lot of light. Before you pick a light, think if the drivers, who may be blinded by incoming cars' lights, will be able to see you. It's best to buy 2 front lights with different modes, including a flashing mode (not a strobe mode though, it's nasty and might be illegal!). Have one in constant, and one in flashing mode.

There are countries where it's illegal to use any flashing lights on bicycles. Know the law in your country before you buy your lights.

Rear lights should be powerful enough to be seen hundreds, not tens of meters away. I think it's best to have two rear lights also. One should be blinking, the other one constant. Be aware though, that if these two lights are next to each other, drivers behind you might think you're indicating right or left. So it's best to mount them on top of each other to eliminate any possible confusion. I'm talking from experience! I've heard good things about the Cygolite Hotshot tail light/blinkie.

10. Cycling sunglasses are very useful. They block light and wind. They also stop bugs, sand and other stuff from getting in your eyes. I recommend you get a pair of cycling sunglasses with interchangeable lenses. Usually these come with 3 pairs of lenses in different colors: dark gray for sunny days, orange (or yellow) for overcast conditions, and clear for low light conditions. Tifosi sunglasses have high quality optics and are affordable.

11. Bicycle locks: I usually warn everyone I know not to leave their bikes unattended, even after locking them. A thief with the right tools can force any high quality lock open in minutes. They can do it in seconds if the lock is cheap. Remember, professional thieves have power tools! If you must leave your bike unattended, get two high quality locks: one U-lock, and one cable lock. Thieves use different tools to break different kinds of locks, so it'll be more difficult and will take them longer for them to steal your bike. The cable lock should be long enough to lock the wheels and the frame. Take easy to steal stuff (e.g. computer) with you.

12. You should always take spare tubes, a patch kit and 2 tire levers with you. If you're in a hurry, you can just change the inner tube without patching it. But what if you have a second or even third flat on the same ride? You'll be glad you have that patch kit with you. As for the tire levers, you might be able to take the tire off with your bare hands, but this could be almost impossible sometimes, and it depends on the tire-rim combination you have. So it's better to have the levers just in case. Tire levers are plastic; don't use metal objects to force the tire off the rim, as you might permanently damage the aluminum rim!

13. A tool kit must be available at all times, especially on longer rides. You can buy a multi tool, which is small and light. They are great for emergency repairs. Topeak Alien II is a good quality multi tool, and it has 26 tools in it. Also available at ChainReactionCycles.

14. Gloves might not seem important, but they are for a cyclist! All year round, gloves protect you hands in case you crash, so think about your knuckles! In hot weather, if you have sweaty palms, gloves can prevent your hands slipping on the handlebars. In cold weather, they help you stay warm. In freezing temperatures, fingerless mitts are recommended, or "lobster claw" gloves for better dexterity.

Did I forget anything? Do you have anything to add? I'd love to hear your opinion!