For the classic, pure, viral, social and/or user-generated content businesses -- that will probably be monetized with advertising -- the generic headline metrics like daily/weekly/monthly active users and engagement/retention rate are important. There are just so many new products that attempt to be the next Facebook/Twitter/Youtube/Pinterest that showing that you are already punching through the noise is pretty important.
For two-sided marketplaces (the next eBay/Etsy/AirBNB/Uber) it's most important to have a real theory about how you're going to get both sides of the flywheel spun up. The traction doesn't need to be gigantic but there needs to be a real plan. We still see too much handwaving in this category -- it is REALLY hard to spin these up from a standard start and most simply languish and die.
For ecommerce and ecommerce-like busineses (the next Fab/Ziluly/OneKingsLane/Zulily), the most important thing is showing a model, with initial proof, of how the cost to acquire customers is less than the lifetime value of those customers. For example, in recent years it has become harder to build these businesses based on Google keyword advertising -- search volume isn't growing very fast, and lots of people are trying to acquire customers in most categories, and so keyword ad rates often get bid up to just past the point of unprofitability (the delta is the amount of excess funding going into businesses in these categories). So creativity on customer acquisition -- and showing that in economic terms -- is key.
I think that a credible team with any of this in reasonable shape from a seed round is not going to have trouble raising an A in this environment. But for those that have already raised an A, it has become really critical to have these factors nailed (whichever are appropriate) to be able to raise a B.
Finally, probably obvious but worth saying -- investors are all over the map on all of this stuff all the time. It's very valuable to be able to prequalify investors for interest and knowledge about particular categories -- and frankly IQ and judgment -- prior to meeting with them. Good advisors and angels can be very helpful with this. This is also why we try to be transparent on these topics (such as with Scott's interview) -- better for us and for entrepreneurs to know how we think before they walk in the door.