In the U.S., at least, it's not uncommon to hear: The light bulb is burned out .
The expression can be found in writing sometimes, too.
ell.stackexchange.com/users/113/J.R.
I'm also in the U.S., and I agree with J.R.'s answer, but I also find myself saying:
The [light] bulb went out.
"Went out" is more general, so you can say "the lights went out" during a power outage even if the bulbs are still fine, but if I say a bulb went out, it usually means I need to replace that particular bulb.
ell.stackexchange.com/users/230/snailplane
I'm in the UK and the most common expression I hear (and use) is that "the bulb has blown".
I'm not sure why we say this, when it doesn't really blow, it just burns out, but it seems pretty common around here (NW England).
ell.stackexchange.com/users/962/Danny Tuppeny
As a native speaker of British English, I'd say
The bulb's gone .
ell.stackexchange.com/users/217/Barrie England
I am 42 years old and from the east of England.
I would say the light bulb has "fused".
I learned English from people born before the 2nd world war in general.
People used to say "fused" because of the similar mode of failure.
A old fashioned light bulb and a fuse share a lot on common.
Both have a fine wire encased in a sheath.
Both fail in a similar way.
The wire breaks inside.
Hence fused.
Sometimes light bulbs do shatter when they fail.
In that case it would be more appropriate to say the bulb has blown.
When light bulbs shatter as the failure mode then there has probably been a power surge.
If you are interested I can tell you more about tungsten light bulbs and old style wire fuses.
ell.stackexchange.com/users/30593/David May
I'm from the U.S. and have heard multiple ways used commonly.
If you are holding a light bulb that no longer works because the filament is broken you could say: This light bulb is burned out.
This light bulb is blown out.
This light bulb is dead.
If someone wants me to fix a light that won't turn on, they'd typically point at it and say: That light bulb burned out!
That light bulb has blown out!
That light bulb has died!
That light bulb went out!
Typically I am in a better mood if they say "Would you fix it, please?" afterward.
I've heard "...has burned out" and
"...died" with about the same frequency, but "...blew out" seems less common.
Also, "That light bulb went out!"
is common, but I've rarely heard it used to describe the broken state of the bulb, "This light bulb went out.
" makes sense to me, but "This light bulb is gone out." or some other similar construction for the present-tense would seem unusual to me.
ell.stackexchange.com/users/8824/RaisedInMinnesotaUSA
The bulb's (has) fused!
This is what I've always heard and used. '
blown' sounds strange and american.
I supose 'the bulb has gone/the bulb went'
needs some thought before being understood.
ell.stackexchange.com/users/49277/praestans
Lets say, I want to tell my roommate that one of the lightbulbs has stopped working, I usually say    The light bulb is  gone  or  broken down .   I did some search related to these expression and it seems that they are not very common and will sound odd to the natives.
How do native speakers say 'the light bulb has stopped working'
ell.stackexchange.com
<word-request><phrase-request>
ell.stackexchange.com/questions/3709
ell.stackexchange.com/users/893/Thor
There are a number of expressions: This light bulb has burned out; This light bulb has blown out; This light bulb has died; This light bulb has fused; This light bulb went out; This light bulb is dead; and This light bulb has gone. Burned out, blown/blown out, dead, fused, died, went out are all options.
Burned out, blown/blown out, dead, fused, died, went out are all options.