https://en.wikipedia.org/wiki/2019_European_Parliament_elect...
However they're primarily just groupings of like-minded national parties.
The EU has what's called a "political party at European level", there are 10 of these registered and a few more that don't meet the criteria to register.[0]
Most of these parties - and in particular the biggest two, the EPP[1] and PES[2] - don't allow individuals to become members.
Instead their members are political parties at national and regional parties that already exist in the member states.
One or two of the other parties are built around member states' parties, but also offer individual membership. ALDE,[3] the third-largest party, is one that does.
There are a few more parties that are active but don't meet the criteria to register.
The Pirate Party,[4] already mentioned by others, is one, but that too is a party-of-parties.
Volt Europa[5] is probably the only serious attempt at creating Europarty that is comprised predominantly of individuals, although even they allow for national-level parties as members in their statutes.
What can make things slightly confusing is that in the European Parliament MEPs don't actually formally sit as parties, but rather as political groups, of which there are 7. There are MEPs that don't sit in a group, but these tend to be more fringe parliamentarians, typically on the far-right.
The EPP and PES are big enough to have groups (EPP and S&D, respectively) that are more or less coterminous with their parties, but the other parties work together.
The European Greens sit with the European Free Alliance[6] along with the Pirate Party and Volt Europa, for example.
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[0] Regulation 1141/2014 [7] lays down the requirements. Amongst the details of the legal restrictions that have to be adhered to is the requirement to have elected representatives, or achieve 3% in European Parliament elections, in at least 1/4 of the member states.
[1] The European People's Party (EPP), this is the party of both the current Commission President and Merkel: https://www.epp.eu/
[2] The Party of European Socialists: https://www.pes.eu/en/
[4] https://european-pirateparty.eu/
[5] https://www.volteuropa.org/
[6] These are mostly sub-national regionalist and/or separatist parties. https://www.e-f-a.org/
[7] https://eur-lex.europa.eu/legal-content/EN/TXT/?uri=CELEX:32...