If your site has good content and if you submit a few articles to digg,etc and also if you submit a sitemap to google... it will take 1-2 days to index.
It takes time depending on how well you optimized the content of the site using your targeted keywords and how competitive is the keyword.
Exactly the same length as this piece of string If you've got a link lying around somewhere it crawls frequently like digg or digitalpoint - within hours. If you have no backlinks and don't submit it. Never. So, depending on how easy you've made it for a search engine to find it, between an hour and never.
honestly I still think is about the '' jobs '' wich google boots are doing . Isnt about the links ( atleast not the backlinks from other popular sites ) .... I had experience with one domain name who was fresh registered but with good keywords on name ... just a short and sweet name . was on google within a hour or so ... had also experience with another domain focused high payd keywords used to install and develop wordpress ( submited sitemap and other stuffs wich peoples usualy think they help .... ) took arround 6-7 days to show up on google .... so my opinion is depend only by the '' jobs '' example if you are trying to index on google '' make money online '' domain name with similar content ... will take longer becouse the crawlers probably first trying to finish the curent job wich are to crawl enstablished sites ... and only after that you will be crawled and indexed . its all about a simply game - first come first served ... you like a new one arent first come so you will be served '' sometime '' !