Just go to the relevant directory and type:
python -m SimpleHTTPServer 8081
or whatever port you want, and you can then go to http://localhost:8081/
(Slightly longer explanation at the Linux Journal.)
This can be especially user because some browsers are a bit weird about loading stuff from the file system, you run into odd cross-site-scripting style issues, like if you try to load a static ".json" file or what not.
There's a variant if you want to run scripts:
python -m CGIHTTPServer 8081
It's pretty old-school; you make a cgi-bin directory under where you will run the command. Your scripts then have to start with #!/usr/bin/php or whatever, and have execute permissions.
Also I just realized (duh) that PHP has its own webserver-
php -S localhost:8000