OK, so you've got your new bike, what accessories do I need to buy? First you need a good pair of cycling shoes, there are many on the market, road bike or mountain bike or you could get some touring shoes that you could walk in as well as cycle.
You cant ride in the nude so you'll need cycling clothes, again there is a lot to chose from, depending on what you're going to do and where you're going to do it. Obviously warm weather is easier, shorts and a jersey; cold weather means more clothes, gloves and a hat.
Accessories For My Bike
So your ready to hit the road or tracks, what more accessories do you need? Well you will get thirsty, so you have to carry something to drink, most people have a bottle cage on there bikes, these are made of either steel, alloy, plastic or carbon fibre. The cage
bolts onto the bike and there is a special bottle fits tightly in the cage so it doesn't fall out over bumpy terrain.
Some people prefer a Camelback, this is a liquid holding bag that you wear on your back, it can be on its own or incorporated into a small rucksack, so you can carry other things like food, extra clothes or tools for any mishap. Both systems are good and each has advantages, you will need one or other to carry your drink or you could get dehydrated, even in cold weather.
Cycle Computers. 
Its nice to know how far you have traveled and how long it took you to do it, so you need one of the most interesting accessories, a cycle computer. There are many, the basic records your speed, time and distance and are fairly cheap, or you could buy the top of the range computer that will tell you: - distance, time, speed, altitude, pedal revs, pulse, power output and steepness of the climb, these computers you can download to your home computer when your finished your ride and print off your ride results.
Glasses
It's a good and cool idea to wear eye protection on your bike rides, first they keep the sun out of your eyes on those hot days, but also they can stop grit and flies from blinding you and they are a cool fashion accessory.
Oakley was probably the first and now the most well known manufacturer of sports eye wear. There are others, like Rudy Project, Adidas and Briko, you can get cheaper glasses with replaceable lenses, clear for bad weather conditions, dark for the sun and reflective for just posing, they do the job for the money, but do they have the same street creed?
Other Accessories
You can put racks on your bike if you want to go touring to carry clothes and maybe even a tent with pannier bags. With mountain bike you can have bar-ends for more hand positions. A stand so you don't have to lean your bike against a wall, chain guards, small bags, pumps etc. etc. There are a lot of different accessories, but they all add weight to your bike and that came make more hard work on your bike ride.
How to submit your Cycling Question?