Here's a few cases which I've found that competition doesn't matter:
* Competition is ugly.
* Competition is hard-to-use.
* Competition is broken to some extent.
* Competition is not solving the pain.
In these cases, ignore the competition, it doesn't matter. But some cases, I think competition does matter. If the competition really is doing a great job at solving the pain, has reached a significant scale, and isn't doing any of the above, then it does matter.
I think Mint.com is a beautiful product, easy-to-use, works well, and solves the pain. Competing against Mint as a new, better financial service would be very hard, because its hard to be an order of magnitude better. Some would argue that it is broken to some extent.
Dropbox is beautiful, easy-to-use, definitely not broken, and solves the pain. All others before it were hard to setup, or didn't work well, or didn't solve the real pain (e.g. Microsoft's 6GB filesize limit). I bet Receivd will be good because Dropbox doesn't solve the exact same pain that Receivd is, at least for how I understand it.