There are basically two types of cars James Bond drives. The ones provided by Q-branch, and the cars 007 ends up driving, due to escape or pursuit. Following are all the cars James Bond has used over the past 35 years.
 

 

Cars provided by Q-branch
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Aston Martin DB 5
Probably the most famous of all Bond's cars, the Aston Martin DB5 (registration number LU 6789 or BMT216A or 4711-EA-62). It appeared in Goldfinger, Thunderball and for a  brief high speed race in Goldeneye (registration number BMT214A). Q's modifications included two forward firing machine guns, smoke screen, oil slicks,  an ejector seat  and radar tracking system. A bullet proof shield protected the rear window, while revolving number plates made the car untraceable.

 DB 5
DB 5
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Lotus
Lotus Esprit

Lotus Esprit
Lotus Esprit (registration number PPW306R). Featured in The Spy Who Loved Me. Equipped with surface-to-air missiles, depth charges, rear firing mud sprayers, underwater smoke screens and torpedoes.  Bond also had a white Lotus Turbo Esprit (registration number OPW 654W) in For Your Eyes Only, but the anti-theft device incorporated by Q-branch was perhaps a little too effective. Later in the film, he drove a red Turbo Esprit (registration number OPW 678W).
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Aston Martin V8
Aston Martin V8 (registration number B549WUU) featured in The Living Daylights. Wheel hub mounted laser, spiked tires, stabilizing skis for driving in the snow and turbo thrust where among Q's modifications. Dual forward facing missiles came as standard. Unfortunately Bond was forced to use the self-distruct button on this beautiful car.

Aston Martin V8
Aston Martin V8
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Z3
BMW Z3

 BMW Z3
The BMW Z3 roadster featured in GoldenEye. The roadster was accompanied by all the standard Q-branch modifications like, rear parachute, twin stinger missiles, and an in-board satellite tracking unit.
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BMW 750i
The BMW 750i makes an incredible appearance in Tomorrow Never Dies. Apart from classic Q-branch extras, the BMW operated by remote cellular telephone.  The car was best remembered for its ability to endure the most brutal attacks. The BMW's short life ends with a leap from the top floor of a parking building. Fortunately Q calculated such use by 007 and had prepared a lucrative collision insurance package.

BMW 750i
BMW 750i
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Cars Bond was forced to use

Sunbeam Alpine
Driven by Bond in Dr. No, the Sunbeam Alpine is involved in 007's first ever car chase.

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Classic Bentley
Making its only appearance in From Russia With Love, Bond's classic Bentley is equipped with a car phone which was years ahead of its time.
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Aston Martin DBS
George Lazenby in On Her Majesty's Secret Service, drove the Aston Martin DBS. A classy six cylinder edition from the Aston Martin DB series released in 1969.

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Mustang
Mustang Mach I

 Mustang Mach I
Featured in the main car chase in Diamonds Are Forever, the Mustang Mach I raced around the streets of Las Vegas performing some incredible stunts. Perhaps the most remarkable was an escape through a narrow alley way, in which the car drove on two wheels.
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AMC Hornet
The AMC Hornet was commandeered from the local AMC showroom by 007 in The Man With The Golden Gun. The Hornet was particularly memorable for performing the incredible 360 degree mid-air roll over a river, while in pursuit of Fransisco Scaramanga.

AMC Hornet
AMC Hornet
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2CV
Citroen 2CV

 Citroen 2CV
Featured in For Your Eyes Only. Bond used Melina Havleock's Citroen 2CV (registration number M-1026-A) to elude Hector Gonzles' men in Peugeots. Although the 2CV was shot, bumped and rolled down the hillside, it still managed to help 007 and Melina escape.
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Mercedes
A Mercedes (registration number BT 36-72) containing stolen jewelry came to 007's aid in Octopussy when he needed to catch up with a train carrying the escaping villain, Kamal Khan. After losing its tires, the car drove along the train on the railroad tracks!

Mercedes
Mercedes
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Alfa Romeo GTV
The Alfa Romeo GTV made a brief appearance in Octapussy (registration number BT F6 08). Trying to reach an atomic device, headed towards an American base in Germany, 007 commandeered the Alfa from some annoying lady in a village near by. Driving in great style, Bond was able to outrun the German BMW police cars and arrive just in time to terminate the bomb.
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Renault 11
In A View To A Kill, 007 commandeered a French taxi driver's Renault 11 in order to chase an assassin, who made an escape by parachuting from the Eiffel Tower. The Renault had its roof chopped off, and then its body cut in half. Still Bond was able to drive the car to where the assassin landed.

Renault
Renault 11