It depends on three things: which tool, which tier, and what data.
Free consumer tiers often use your inputs to improve their models. Don't paste in confidential, regulated, or proprietary information.
Paid business and enterprise tiers generally don't train on your data and offer contractual privacy guarantees. Read the terms — they vary by provider.
Regulated data (PHI, PII, financial records, attorney-client material) requires a tool with the right protections in place — for example, a Business Associate Agreement (BAA) for healthcare data. Don't assume a consumer chat tool meets that bar.
When in doubt, ask yourself: would I be comfortable if this ended up in a competitor's hands? If the answer is no, don't paste it.