Expensr's special sauce is that it lets you compare your financial picture to other people who are like you, based on tags. For example, say you tag yourself "married," "San Francisco," and "lawyer." Then you can see how much other married SF lawyers are spending on rent, and if you're living at a level above or below your peers. Or you can look up data for other tags, to see, for instance, what engineers in Houston are making. You do have to trust that other users are as rigorous with their Expensr data entry as you are: If you reliably enter in all your dining out expenses, but other users tagged the same as you are do not, then you might think that you're overspending when you're just being more compulsive about your bookkeeping than everyone else. (I couldn't use this feature because none of the tags I tried had enough users to generate statistical data.)
The service has several features that are standard for online financial applications. It's easy and simple to create accounts, enter transactions, and see graphs and charts of where your money is going.
Expensr is easy to use -- much easier than the default financial app for most people, Quicken (the 2007 version of which I found intolerably buggy). While Quicken also offers tracking, as well as nice charts and graphs, getting basic data and analysis out of Expensr is much faster than getting it from Quicken. And if you only have a few accounts, getting data in can be almost as fast, since Expensr reads OFX files from banks (Quicken can automate downloads, though, which is a plus).
However, Expensr runs out of gas before Quicken. It won't pay bills electronically. It is not a solution for tracking investments or the stock options you have in that Web 2.0 startup you're working at for next to nothing. It won't calculate mortgage payments. And so on. Also, people may not want to store financial data on a startup run by a couple of guys fresh out of school (although there's nothing about the site that says you have to attach your real name to your transactions).
What Expensr has going for it is simplicity, speed, ease of use, and cost. It's free. It looks like a solid solution for a young adult's simple finances.