In short: It is probably prohibited by law (assuming most countries have a law similar to the Dutch), and probably also by your ISP. However I don't think anyone will win a court against you if you don't do anything besides portscanning and don't overload the service. Very strictly speaking, typing a random domain in your address bar would be portscanning as well.
As mentioned in the comments on your question, it is usually prohibited by the ISP. This can be your ISP at home, but it can also be in the terms of a VPS hosting provider.
Besides this, I can only comment on Dutch laws really. It mentions the following as "computer fraud": Intentionally and unlawfully entering an automated work, or part of an automated work. Entering is defined as either:
- Breaking security;
- Using a technical procedure;
- Using false signals or a false key, or
- Using a false identity.
Clearly you are not breaking security by sending a packet to test whether a port is open or using a false identity, but a technical procedure is a very broad term. Also false signals can mean a lot, probably including sending packets, especially when you can't prove their purpose besides testing whether a port is open for potential abuse. This would fall in the category of unlawfully entering an automated work, given that you have no permission from the target.
Still though, I don't think anyone would win a court against you for portscanning as long as you don't overload the server. Breaking the security is only done after an open port is found.
Source (Dutch): http://wetten.overheid.nl/BWBR0028570/Tweedeboek/TitelV/Artikel144a/geldigheidsdatum_30-06-2012