Estuve haciendo proyectos y conecte leds de 5mm en pines digitales sin resistencia, encienden muy bien, pero sucede algo malo a largo plazo???
Leds basically are shorts, so you will blow the pins that they are connected to. If you connected them directly to an Arduino, You might even blow the internal power rails in the microcontroller.
Actually, the LED will probably blow first.
The Mega-based Arduinos can take quite a bit of punishment on their I/O pins, I once accidentally shorted a few output pins directly to ground. Chip got pretty hot VERY quickly, but it survived the ordeal without any damage.
So, as long as the LED blows "clean" (i.e. it does not produce a short while burning up), the Arduino should survive. That being said, it is an unquestionably BAD idea to connect an LED without a resistor... 
This multilingual thread?
(I am spaniard)
Regards. Saludos.
Officially, not a multilingual thread because this forum section should always be in English. But sterretje was kind to the OP and responded in English instead of reporting the thread to the forum moderators.
It is also worth saying that there are circuits where series resistors are not needed with LEDs. Some chips that are designed for driving LEDs, for example max7219 and tlc5947, have "constant current drivers" on-board the chips. These act like self-adjusting series resistors. Arduino pins and the outputs of most chips such as 74hc595 do not have these CC Drivers, so series resistors must be used with LEDs in these circuits.
¡Bien por sterretje y PaulRB!
Just in case the OP does not fully understand:
En general no se debe conectar el LED a algo que dé 5,0 voltios; salvo que sean circuitos concebidos para tal fin (último post de PaulRB), se acabará quemando el LED o el circuito. También puede ocurrir aue un limitador de corriente que haya por el camino bloquee el circuito ..)
("Generally speaking, the LED should not be connected to anything that gives 5.0 volts; unless they are circuits designed for that purpose (last post from PaulRB), either the LED or the circuit will be fried. It can also happen that a current limiter on the road blocks the circuit ..")
Saludos. Regards.