Foursquare - Every week or so, I get really addicted to checking into places for a few days. Zhephree's app works very, very well for this task. It makes me wish that our GPS system would work better, since most of my wait time is for the fix. The user interface is very slick.
neato! - Another Zhephree app that's great. I don't always leave this running, but when I need to do some web site debugging, it's very useful. It lets me click on a bookmarklet in my browser and have the page almost instantly show up on my device. It also can be used to send selected text and bring up app pages.
Tweed - It may not be the most stylish Twitter client on webOS, but it's been very stable and nicely maintained, and it serves me well. I don't use the notification feature, as I tend to view Twitter as a pool of data that I can dip into from time to time rather than a email inbox.
drPodder - I like listening to podcasts, but I hate having to manage a desktop client to find and download them. This app does all that for me on the device. The interface is for the power user, but I love the way it uses system notifications to let you pause and resume your track. I just wish I could manage my feed list on the web somewhere -- it would be awesome if you could use the Dropbox API to store your drpodder.xml OPML file online.
SplashID - I was a long-time SplashID user on Palm OS, and I really liked that you could export your records from the desktop to the device. SplashData hasn't done a good job of updating this (where is sync!), but I still always load this up. If I can find a good cloud sync solution that's supported on webOS, I might switch to it.
TMaps - NY - if you navigate around NY, you need a good subway map. You especially need one that works when you're out-of-service. TMaps fits those needs well. I'd really love to see a port of the iPhone's Exit Strategy app which includes street-level apps and advice on where exits are in subway stations, but this will do.
I'm giving myself a bonus selection with Google Reader. I've tried a few of the client apps that use the API to access my Reader feeds, but I keep coming back to Google's mobile website for the best experience. I like that you're instantly synced with Google's own database of read/unread articles, and I like the "open drawer" method of moving quickly through a lot of news items. This isn't a true app, but I usually use the Browser's "Page / Add to Launcher" command to make an icon for it.