For example, a business like eBay has fees which are ludicrous, an interface that is not at all intuitive, but because it was pretty much the first established brand in online auctions, it's what most people keep using.
An "established brand" did get into the mind first... - you might possibly gain ground on them (eBay) by focusing on a unique segment (Esty) or a host of other ways. Getting established is the hard part - being first is not a guarantee you'll end up being the "established brand". Was Facebook the first social site? And while a strong brand name is great to have - easier to remember and easier to market - its still nothing compared to getting critical mass.
First mover is a huge advantage if you manage to create a new segment and then spend all your time focusing on promoting how great the segment is - and hopefully at the same time gaining critical mass.
Yahoo-Google
Friendster-Myspace-Facebook
Blogger-Wordpress
Hotmail-Yahoo-Gmail
I can go on.