Right now it is extremely difficult to build your own web crawler that would compete with Google. And that is not because of the technology, but because multiple sites will prevent your bot from accessing them if you're not Google or Bing - either through robots.txt, or through directly banning your IP if it's trying to crawl and it's not a confirmed google-bot.
Having a non-profit, open source, crawler that keeps an up to date index (or web cache) of the web would help competition spring up.