Here is my main concern:
How do you draw the line between Web App and Website?
For example, I consider Weebly and Evernote to be web apps. I do not consider Digg or Wolfram Alpha to be ... furthermore, some of your listings only partly qualify as Web [Anything]. Dropbox and RescueTime both have desktop components and Skype is truly not a web app/site in my opinion.
I'm not sure how to define it or where to draw the line–I just think you might have more success by focusing your site on true web apps (i.e. browser-based apps or SaaS that replace/compete with desktop apps and solve a personal/business pain point). It will solve minalecs's point of having too many sites to filter through.
As the site is now, I probably wouldn't use it. But if it was truly an app directory where I could say "Hey, I need to do X ... I wonder if there's a web app" then go and find such an app ... then, yes.
Our goal is to make AppUseful straightforward enough to market to the mainstream users. There are already a lot of resources that target the geek community. About half of my friends still don't know about popular sites such as Yelp.
Given your content, clearly separate your ads, or use text ads only. The change-background-on-hover effect is annoying. Use a white background since many logos are not transparent, and white. Remove that thin gray border, it makes the dark-background logos look messy. Your headings are not sufficiently distinct from your website titles (just remove the site titles, which will also keep the site from looking ugly when you have long titles). Put the little (3) vote counter to the left of the stars. Get rid of the dropdowns for sorting, and the buttons for pages.
When I click the logo, I expect to go to the site. I don't really care about your detailed info - that's what (more) is for. I don't want the company's often useless and spammy tagline, enforce a brief and useful description of the site. I don't want to dig around in subpages for information, and I don't want to see a screenshot of the site when I could have been looking at the site itself.
1) Are you planning on making money with this? How? Ads probably aren't the answer. 2) How do you keep users coming back? Once someone finds the app they're looking for, are they likely to visit your site with any regularity? 3) What percentage of users write reviews? If you're like other review sites, the number will be shockingly small. How can you incentivize users to review?
Too many featured/recent/popular; how about only 4 in each, and rotate/fade them in and out, let me then go to the relevant page to see all recent or whatever.
Logo/tag cloud section is a bit too big IMHO. It takes up 1/3 of the window on my work monitor.
Consider Google News' front page: they divide stories into sections (World, Business, Health, etc.) which gives users a high level overview of the content at a glance, a domain context for headlines in a given section, and allows them to easily ignore whole sets of stories they might not be interested in. The iTunes App Store is the same way.
I'm also not sure how useful the Recently Added section is going to be in the long run. The date at which an app was added to the database is less important for users than the date at which an app launched, went out of private beta, etc.
Also, grammar nerd alert from the "About Us" page: "User can submit, rate, and write reviews for web applications that they like." User should be "users."
Is this meant to be an open index of web apps/services? While useful now, like minalecs pointed out, I see it quickly devolving into an index of the internet in general if it gains traction.
OpenID please.