Yes, fighter jets and other military platforms are equipped with self defence systems.
Air to air missiles primarily come in 2 varieties. Radar guided missiles and "infra-red" (IR) optically guided missiles. Radar guided missiles are typically longer ranged missiles, with IR missiles typically shorter ranged and more agile.
Fighters (decent ones anyway) are equipped with self protection jamming equipment and "chaff" (strips of metal foil deployed into the air around the aircraft) intended to jam or disrupt the enemy radar, so that the air to air missile cannot be guided. These are generally termed - Electronic Counter Measures (ECM).
Radar's and modern missiles however are equipped with Electronic Counter Counter Measures (ECCM), which resist the jamming efforts of the enemy aircraft, so it really becomes a contest of who is better, the radar/missile combo or the defensive ECM?
Other defensive options include low observability built into the airframe of the enemy jet. What most people call "stealth".
How a radar basically works is radar suite is fitted with a radio transmitter, a radio receiver and a radio signals processor.
The transmitter transmits a radio signal (the radar beam and they transmit quite a lot of them actually) which bounces back towards the radar system when it hits something. The rado signal bouncing off the object is known as a reflection and works the same way as a reflector on a bicycle - when light is shone onto it, it reflects the light, making the reflector "glow".
The receiver then receives the "bounced" return signal and the radar's signals processor is able to determine range (how far away the object is), bearing (what direction the objection is moving) altitude (what height the objection is) and speed (how fast the object is travelling) etc of the object, based on the known position of the transmitting platform and calculations of the time it took for the transmitted radio signal to bounce off the object and return to the radar suite.
Now, obviously for a fighter aircraft it is a benefit if your fighter is designed in such a way so that these radar beam are not reflected directly back to the transmitting radar, but rather in another direction so the radar receiver is unable to get a good return signal.
There are a number of different ways this is achieved. For simplicities sake, a flat metal plate is one of the best surfaces for reflecting a radar signal. Older fighter jets were made simply of metal and provided enormous radar reflectivity returns. They were very easy to track by radar.
So fighter designers began experimenting with different materials than metal to see what a modern fighter jet could be constructed from that provided the strength, or more, of metal, without the radar reflectivity. This research led to composite materials, which provide a significant reduction in radar reflectivity and most modern fighters are constructed significantly from these materials. They are also known as "radar absorbent material". (RAM).
What these materials do, as the name suggests, is absorb the radar signal, rather than reflect it, meaning that less of the radar beams are reflected back to the radar, making it harder for these aircraft to be tracked by radar.
Designers also discovered that by changing the shape of aircraft to specific shapes, they could also reduce the radar reflectivity of an aircraft, by "scattering" the signal in directions other than those which are optimal for the transmitting radar.
These ideas led to develop of the F-117 "stealth fighter" which demonstrate a radically different appearance and yes, flying qualities to other aircraft, but which also demonstrated an outstanding level of "stealth" and proved repeatedly, very difficult to track and engage by hostile defence systems. This is the aircraft I am talking about, the F-117:
http://www.product-reviews.net/wp-content/userimages/2008/03/f117-stealth.jpg
The other main means by which a missile can track aircraft is in the "infra-red" or ultra-violet (or both) spectrum of light (radiation). Some missiles are equipped with "staring arrays" not dissimilar in function to digital cameras which "see" in the infra-red/ultra-violet spectrums of light, which shows very hot parts of aircraft against the background radiation. Hence these missiles are sometimes known as "heat seekers". Here is an example of what I am talking about, what an IR missile sees:
http://www.ausairpower.net/000-ASRAAM-4A.jpg
Because of their "staring" method of seeking a target, the IR missiles are usually fairly short ranged (up to about 18k's). They are generally fast to be launched and are very agile because they have to perform very tight turns at high speed and at close range.
Good fighters possess methods by which they can defend against these missiles. The most common method is by the use of flares which are deployed by the aircraft around itself. These flares are tuned to match the heat characteristics of the aircraft carrying them in the hope that the missile will track the flares instead of the aircraft, allowing the aircraft that has deployed the flares, to manoevre (fly) out of the missiles path.
Aircraft also employ specific manoevres when missiles are fired at them. The reason for this is because air to air missiles are very fast, but in order to have agility and for the aircraft to be able to carry many weapons, they are relatively small by weapons standards. This means that the missile's rocket motor can only burn for a certain amount of time and missiles, particularly longer ranging missiles, fly a large proportion of their flight in a "glide" mode because their rocket motor has burnt all it's fuel.
The missile then has a lesser ability to manoeuvre, so what pilots try to do is fire their missiles at the enemy aircraft so that the missile engages the aircraft in what is known as a "no escape zone". Basically this means a portion of the missile's flight where it is extremely unlikely that an aircraft will be able to manoeuvre out of a missiles path.
As you can see therefore, there is a constant "battle" between designers of radar, missiles, aircraft and aircraft counter-measures (flares, chaff, jammers) and pilot tactics for supremacy in the air to air battle.
New tactics and equipment are devised constantly to counter new threats and aircraft are constantly in different energy states, have different fuel levels (more fuel you have, the faster you can go because you can use your afterburner more) etc.
Hopefully this gives some insight into these matters. It is a VERY complicated area...
