Browsers will download up to 6 files in parallel from the same domain: http://www.browserscope.org/?category=network&v=top
This includes stylesheets, images, and so on. For optimal performance, you should combine resources to make sure that no more than 6 (parallel) requests are needed to load everything on the page. This means combining script files, combining images into CSS sprites, combining stylesheets and so on. If you need to load more, you need to split the requests across domain names.
As far as minification, it depends on how big the file is. Minifying a small file won't give much advantage, but minifying a large file can make a real difference on slow network connections, even when combined with gzip compression. See http://stackoverflow.com/questions/807119/gzip-versus-minify
Solutions like requirejs are meant for loading scripts not needed to initially show the page, but needed instead to interact with it. Even there combining scripts is recommended to stay under the 6 requests threshold.