Keef,
You don't have to have an index.html, but if you don't then anyone entering just www + your webspace name will get a "Can't find it" error.
Actually, strictly speaking you can have whatever you want as long as your web server is correctly configured to serve it as a default page when none is requested for a directory.....
And in relation to P.P's post...
If the organisation which provides your hosting and stores your web files is asked to host more than one webspace name then you need a folder in your webspace for each web title, each containing a different index.htm file. Your host is then instructed to direct calls to each webs title to the appropriate folder so that, despite being hosted by the same server, each webspace name appears independent as the appropriate index.htm fie is opened in each case.
A process which could be summarised thus when you are asking your hosting provider to set it up :
"HTTP/1.1 Name-based virtual hosts."
Something which any hosting provider worth their salt should be able to provide in this day and age (and for which I would not expect to pay any extra).