Massive email bomb / inbox flooding, is my Gmail compromised?

Today I suddenly started receiving 3–4 emails per minute, and my Gmail inbox/search count has reached 12,000+ messages.

The emails are coming from completely unrelated websites and countries/languages. Examples include:

• French businesses sending contact-form confirmations
• Japanese businesses saying an inquiry was submitted
• Spanish websites confirming contact forms
• Greek websites saying an account was created
• Pakistani websites sending account-registration confirmations
• Other random shopping/service websites
• I also received a random Google Calendar invitation

Some of these are clearly showing my Gmail address as the email used to create an account or submit a contact form.

For example, one email from a French soap company basically says: “Thank you for contacting us. Your message was received successfully.” I never contacted them.

How to stop or minimize this subscription emails?