I am a web and iOS developer. On mobile, we have famous tools to collect all the exceptions and errors that application throws.
There's Crashlytics (and others) that, with few lines of code to install the sdk, start tracking everything automatically. Then they display the error and useful information on their website with priority and other stats.
Is there anything like that for web applications? Or explicitly for php or js apps?
www.exceptional.io is exactly what you're asking for. It costs $9 per month after a free trial.
Integration with PHP is done by including a wrapper and a couple of lines of code: https://github.com/ankane/exceptional-php/
It can also be integrated with javascript with a couple of lines:
<script type="text/javascript" src="http://js.exceptional.io/exceptional.js"></script>
<script type="text/javascript">
Exceptional.setKey('your_api_key');
</script>
Another option is New Relic, although it does a lot more than purely error logging - it provides all kinds of server monitoring metrics. https://docs.newrelic.com/docs/applications-menu/errors-dashboard