I am certain that Karol's solution is correct (the RewriteCond in solefald's solution is unnecessary), and respectfully dispute TMG's rebuttal regarding PageRank.
First, SEO and PageRank: while it is true that Matt Cutts has indicated that a 301 redirected page is not (quite) as powerful as a direct link, the condition that needs to be corrected here relates to duplicate content. If the site with /index.php and the site with / result in the same page, this is duplicate content, and (especially with the home page of a site) is an important consideration: a given page should always have one and only one URL, the "canonical" URL for a page.
At best, Google will ignore whichever one it decides it should. At worst, it will index both and sites linking to one variant will pass PR to that variant, and those linking to the other will pass their PR to the other. You should get all pages to link to one (and the one should be /).
Karol's solution above is correct (you do not need a RewriteCond) with one minor note: if you are editing a .htaccess file, it's right as written; if you are editing in the server configuration file or VirtualHost context, you'll need to add a slash first
RewriteRule ^/index\.(php|htm|html|asp|cfm|shtml|shtm)/?$ / [R=301,L]
or to make this work in either context, use the ? regex operator to say "possibly a slash":
RewriteRule ^/?index\.(php|htm|html|asp|cfm|shtml|shtm)/?$ / [R=301,L]
A final additional point: make sure in your configuration (either server, virtualhost or .htaccess) you specify at least: