I've read all the answers and I agree with them but aren't totally right, so I decided to write mine too.
First of all, as @CristiC777 pointed in his message, if you reach the case where you need to break a for, you are doing something wrong before this point. You probably can fix this just putting a limit on your queries or unsetting data from your arrays. This is a better solution because you will improve the response time and save server memory.
Twig views need to be silly. If you put a bunch of conditions and variables into them, you will only make them unreadable and unmaintenable.
If, for some reason, you cannot change the previous code, as @Edgar Alloro pointed, Twig allows you to put conditions on a for (since 1.2). Your example will change to something like this:
{% set keepFor = true %}
{% for value in array if keepFor %}
{% if value != 'valueExpected' %}
{% keepFor = false %}
{% endif %}
{{ value }}
{% endfor %}
You can also do your own implementation, specially if you don't have Twig 1.2. If you have Twig 1.2 or above I do not recommend this because the for will iterate the entire array and you will spend more memory:
{% set keepFor = true %}
{% for value in array %}
{% if keepFor %}
{% if value != 'valueExpected' %}
{% keepFor = false %}
{% endif %}
{{ value }}
{% endif %}
{% endfor %}