Yes, both at the EU level and also in many countries (EU and non-EU), see:

https://en.wikipedia.org/wiki/European_Citizens%27_Initiativ...

https://en.wikipedia.org/wiki/Popular_initiative

"Some threshold" is doing a lot of work here, since the requirement is a million signatures (which also need to be from multiple countries).

I made a small mistake, the response will be from the Commission, not Parliament, because only the Commission can propose laws anyways - but you do get a hearing in parliament.

But essentially, even crossing the million signature threshold doesn't win you anything but a slightly bigger soap box and the promise of the Commission giving you a "no" in writing rather than just ignoring you. There is no requirement to actually act on it, and no way to force it (unlike e.g. in Switzerland where actual binding popular votes can be initiated with enough signatures).

We have this in the UK too,but it's a waste of time.

You just get a stock/automated response to most petitions.

That said, they are required to set aside some parliamentary time for it and for petitions to be "debated".