Q: Is it illegal to watch movies online? Without downloading anything.

A: Watching itself does not constitute copyright infringement. Using a reference to a colleague who previous used this example, you are not infringing copyright by watching a band perform cover songs on stage.

However, copyright infringement in the United States is a strict liability offense. Meaning, that a user is liable when they illegally copy works, even if they're not aware that this is wrong, or that the work is protected by copyright.

Watching a film online, via download or streaming, would constitute infringement because your computer is making copies of the copyrighted material. Via streaming, (if this is indeed the method of viewing), you computer is copying the video files (albeit temporarily in "cache") for purposes of near-simultaneous viewing. However, on 5 June 2014, the Court of Justice of the European Union (CJEU) ruled that streaming illegal content online is legal in Europe, and the most recent US case law refers to either file-sharers (who download) or the host sites (for contributory or secondary infringement).

So, this not to say that streaming movies online is legal. It just hasn't yet been decided and most of the effort is directed towards the hosting sites and not individual users. There is still much debate, so to be safe, you should probably stick with mainstream sites like Netflix and Hulu who have license agreements and procedures in place to secure their right to store and distribute the copyrighted content.

DISCLAIMER: Please note that this answer is not a solicitation, does not constitute legal advice and does not create an attorney-client relationship with myself or the Law Office of Mark B. Saku PLLC. This answer should not be relied on since each situation is fact specific, and a lawyer should always be sought out directly when a legal question arises.