I've been wondering this for a while now, and maybe it differs based on the TYPE of link. But generally speaking how long does it take for a backlink to show up in Google?
Dofollow Blog Comment?
Forum Sig Marketing?
Another Blog? (such as a guest post)
Solution - 1
It will depend on how often google crawls the site you have your backlink on. For example something like ezinearticles or hubpages tend to get crawled by google fairly often so you can expect your backlinks to be picked up in a day or two.
Also, be aware that on something like hubpages, you need a mimimum hubscore to get a dofollow link.
Twitter is indexed fairly fast as well, however most links in tweets are nofollow as far as I know.
You can check if google has indexed the page you have your backlink on by searching for the exact url.
Yahoo site search can be fairly good for finding what backlinks a page has.
Solution - 2
A few days to a week (tops) for nearly anything on the web.
Solution - 3
It's a few days. Once you use Google alert (http://www.google.com/alerts) you can tell when Google indexes it. I know for sure that tweets are indexed within 24 hours.
Solution - 4
It doesn't tend to take that long at all. Especially with WordPress blogs as they are generally very SEO friendly.
A blog which I started at the weekend is already in the search results so I think the safe answer would be 'less than a week' minimum?
Hope this helps!
Solution - 5
The fastest way? do this: make a blog on blogger, add an article with link for your site and ping it here: [[LINK href="http://blogsearch.google.com/ping"]][[/LINK]]
Let me know.