SARH missiles like AIM-7 and R-27 should launch one by one.If the 1st missile don't reach target,you may not fire the 2nd missile.
but AIM-120 or AIM-9 and R-73 can be launched many at same time.
sorry for my english.

AIM-120s are launched all over the place in multiplayer. Hence the term 'spamraams'. Give us flanker pilots a break eh?.

Even active guided AMRAAM class missiles are fired initially under aircraft guidence, active missile guidence is "switched on" as the missile nears the target. This is because relatively small missiles cannot mount sophisticated radar avionics capable of defeating ECM measures and effectively targeting an evading, high powered aircraft.

The "fire and forget" ability of actively guided missiles is typically engaged once the missile itself has a solid lock on to target, part way there, at which time the control aircraft can break away. This can happen fairly quickly in modern air combat, especially at closer ranges.
But contrary to popular belief, a missile lock is far from being a secure kill even with AMRAAMs.
Once the missile is under its own guidence it is prone to ECM measures and outright erratic behavior in an evading, high speed target. The closer you get it to the target before breaking away, the better.

Modern radars are capable of tracking and simultaneously engaging a number of targets regardless of the guidence system carried by their missiles. The Tomcat for example, which has a very sophisticated avionics/weapons package, up to 6 seperate targets may be simultaneously engaged with semi-active and actively guided weapons alike.
I believe most pulse doppler or multi phase equipped fighters can simultaneously engage two. The Eagle and Foxhound 4.

During the Vietnam experience with F-4 Phantoms, it was common practise due to the questionable reliability of early fire-control radars and Sparrow missiles, plus the lack of an internal gun for dogfighting, to release slavos of 2-4 AIM-7's or IR AIM-9's at targets to increase the chances of one of them hitting a manoeuvring, high speed MiG (success was greater with Sidewinders under the conditions they were commonly engaging).

The situation improved markedly with the inception of pulse-doppler lookdown-shootdown technology and improved missile variants.

Nevertheless any aircraft is capable of releasing every missile it is carrying by way of weapon selection, at one time.
Just that how many targets they can chase depends on the control aircraft's avionics capabilities and a bit of luck.