"When I do good, I feel good; when I do bad, I feel bad, and that is my religion." - Abraham Linoln
That sums up how I feel about Blackhat SEO and some of the techniques employed in redirection. Using Wikipedia as a reference to keep this simple, some methods and uses for redirecting domains and traffic are explained.

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301 and 302 Redirects
The most important redirect for SEO is the 301 or 302, when you move or remove a page/domain either permanantly (301) or temporarily (302). The obvious need for this in keeping search rank is not letting the search engine find a 404 when a page no longer exists, serious mods are going on or the domain is moving. One cool senerio is during holidays when you want custom graphics and content for an event, holiday or occasion. Instead of uploading a new replacement page, then reuploading the everyday page, you simply redirect traffic with 302, letting the searchbot know the change is temporary, don't drop my other page, it's coming back. It's been our experience that keeping the old file in place, which keeps the date of when the page was last uploaded to the server improves it's reputation with sites like Yahoo. There have been mixed results, mostly negative, if a temporary page replaces the current one, then the current one replaces the temporary, making the older content look like a new page again because of the time and date the server shows when you could have used a 302 and maintained the last updated time and date. Basically, aging for a page and content can be important.

As a side note, 302's can come in handy if you need to replace a poorly seo'd page name with one that reflects the keyword or phrase and you want to test it. If it preforms better, you switch to a 301 and life goes on. On the 301 side, you are telling the bot that the other page is history, don't go there anymore. An evil use of the 302 is called cloaking and without explaining how, let me just say that plane fare is in a savings account for the next time someone bumps our pages with our own content. moving on...

Short URL Redirection
Also referred to as an alias, the mass appeal of social networks has made shortening links to articles and other pages in websites that we want to share more popular. Mostly, we want as much room to get our point across or create enough interest to motivate readers to visit the content. Since sites like Twitter allow only so many characters of text, if your favorite link of the moment also happens to be as long as your arm, you'd want to be able to post a link, but not as long as it is in the browser address window. Sites like bit.ly, tinyurl.com and str82u.com provide the alias by giving you a short link based on their domain. When someone clicks that shortened URL from another location, like your Twitter page, they are taken first to the redirection site, where the corresponding web address associated with the alias is pulled from a database, then redirects our user the intended location. Pretty neat, eh? The only possible negative result of this is simply referring to the actual page without a keyword link or propler page title/name but to date there haven't been signs of punishment or loss of rank of position for pages we've redirected to any more than using just the domain name in the link text. That's not a concrete rule, just an observation. "Tagging" the converted link you get from us gives you the opportunity to add a short keyword to it, but this is also something that hasn't shown positive or negative effects on SERP. A link is a link but some search engines may not associate that way, judge for yourself and if you see a drop in popularity, stop doing it.

In Conclusion...
Through all that, we pretty much covered the basics and most important aspects of redirecting, more advanced techniques are employed for different reasons, but as a bit of advice to anyone who is marketing or using affiliate programs; don't alienate people by deceptive or spammy practices by hiding junk behind a cute, short link that doesn't reveal the destination without following it. It takes time to build a reputation but only seconds to destroy it. As hokey as it sounds, with all that search engines like Google put into filtering out spam and trash, it seems that understanding best intentions forms in the algorithms. If you are honest about what you are doing, at least that can't be held against you, or more importantly your site. But if you can't help yourself, Thanks! It builds loyalty with the folks that find us.