Wikipedia has a list of lightweight web servers
lighttpd seems popular.
If by portable you mean executes from a USB Flash drive - you'd have to check. Wikipedia lists several portable HTTP servers including XAMPP
and The Uniform Server
XAMPP requires only one zip, tar, 7z, or exe file to be downloaded and run, and little or no configuration of the various components that make up the web server is required. XAMPP is regularly updated to incorporate the latest releases of Apache/MySQL/PHP and Perl. It also comes with a number of other modules including OpenSSL and phpMyAdmin.
Installing XAMPP takes less time than installing each of its components separately. Self-contained, multiple instances of XAMPP can exist on a single computer, and any given instance can be copied from one computer to another.
It is offered in both a full, standard version and a smaller version.
The Uniform Server (or UniServer) is a free open source WAMP package for Microsoft Windows, comprising a pre-configured setup of complementary open source web server tools, the Apache HTTP Server, the MySQL database engine, and scripting languages PHP and Perl. It is released under the BSD license.
It can be activated without any installation, is self-contained, and the package itself is under 10MB. For these reasons, it is commonly used to test web applications on Windows, and can also be set up on removable media for a portable web server. Because it is also designed for security, it is also usable for actual websites.