How can you increase the traffic on my website?

Driving traffic to your website is really about distribution, which could take a few different forms for web startups:

1. Search. The advantage here is that it's easy & plentiful, if you can create unique content. Lots of content is virtually guaranteed to get uncle Google to rain down traffic upon you. But this is a trap for all but the very largest sites that can truly scale content creation for small cost. The disadvantage of this traffic is that it's inevitably low engagement -- usually no more than 2-3 pageviews per visit on average, and rarely leads to repeat use - not unusual for search-driven sites to have less than 20% of their traffic each month as repeat visits. Sites that rely on search traffic are like sieves -- lots of flux through the system, but you never really capture someone and make them your own. And if google stops sending you traffic, the game is over and there are few returning visitors.
2. Partnerships. Integrating your content / functionality into other sites that have existing traffic can help drive traffic to your site, both in its own right, but also by increasing your search traffic (b/c the links back are valuable from a search perspective). The challenge with partnerships is finding an integration that is compelling enough to the partner that they will promote it well, but at the same time, there has to be a real reason for users to click back to your site (often something the partner isn't all that interested in). Integrations that are below the fold, buried in sub-sections of the site, etc will almost never perform, even if it's a big-name partner -- if you can't get the right level of promotional commitment, the deal probably isn't worth the effort.
3. Social / high viral coefficients. This is risky. Almost every new website thinks their users will tell all their friends about them. This almost never happens, but when it does it's because there is real and tangible value both to the refer and referee (the latter is often overlooked - few people are willing to spam their friends for a few bucks. But if they think their friends will like them for sending this along or will be grateful, it changes the game dramatically). Having a product that is inherently social, and making it easy for users to reach out to their friends (perhaps doing it for them - the way quora suggests you post your answers to twitter), but there needs to be a reason to do this that's compelling.
4. Press. This is even riskier. There are definitely startups that have grown in large part because of press -- see Mint (How did Mint acquire 1.0m+ users without a high viral coefficient, scalable SEO strategy, or paid customer acquisition channel?). But the kind of press that matters isn't one-time, big-article-about-our-launch press -- that traffic is huge for 3 days and then gone -- the only kind of press that makes a difference is stable, continuous press -- you have to become a part of the larger conversation so that you aren't getting one big article a year, you're getting articles every week. As a result, press is usually something that fans the flames once you already have a lot of traction. Until you have traction, it just isn't that great a story, even if your product is awesome.
5. Paid marketing. This works incredibly well if you can, early on, calculate / demonstrate an ROI for a user acquisition. If you *know* for certain that you can make $10 on a user, on average, in year 1, then you can feel very confident paying $10 to acquire a user (and VCs will fall over themselves to provide you the working capital you need to do just that). Paying for traffic before you fully understand this ROI is a fool's errand.

With all of this, the ability of your product to capture / retain a user is an enormous multiplier. Let's say 65% of registered users stay 30 day active, and with the flux of new traffic to your site, you can register 50K users a month. In a year, you'll have 400K users in the last month. If only 5% of your registered users are 30 day active, you'll have only 25K of them 1 year out...

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