Not normally, but there are some lock screen apps that might give you what you want. I prefer how Android does notifications to how iOS does it. There are some improvements they could make (and I think they're making them in upcoming versions), but overall I'm quite pleased.

My list of apps I use, only some of which I use frequently, in no order at all:

• Doggcatcher: okay, I lied, this one was put first on purpose. It's my most-used app, and a must-buy for people who are serious about listening to podcasts. I adore this app and use it every single day. The developer is responsive and constantly improving the app, and has added tons of great features and customizability.
• Tweetdeck: post to Twitter and/or Facebook from the same app/widget
• Scoreboard: for sports scores - previously the absolute worst Google-developed app because it never worked - it seems they've fixed it because it works like a charm now
• Google Reader: like Dan said, this is the best Reader app for Android
• Email to Self: my most-used app - all it does is put an icon on my home screen which, when pressed, brings up an email composition with my own address already filled out - it's my #1 productivity tool and I live by it
• IMDb: I may have been wrong, this might be my most-used app, because every time I'm watching TV or movies I have a need to check what the people on screen have been in before
• Soundhound: it's just like Shazam, but I like it more for reasons I can't explain...
• ZipList: combined with an account for their service, it's making dinners easier to plan and shop for. I haven't used it long, but it seems to be just what I've been looking for in a grocery shopping app. I save recipes on their site, and when I plan on making one, I add it to my shopping list and remove the ingredients I already have. I then tell it which of my grocery stores I'm going to and because I've told it the order of the aisles, I can dash through the stores!
• Power Control Plus: kicks the ass of the power control widget that comes with Android. It's fully customizable and can toggle pretty much anything on the device. For example, I have one button on my widget that toggles between WiFi off, WiFi on, and WiFi hotspot.
• Google Voice: for everything Dan said. I love having free SMS (I don't have a plan with my carrier), and voicemails for both of my phones go to it instead.
• Retro Camera: most of the effects it adds are awful, but I like the last one for some interesting shots
• SDWatch and SDMove: developed by our very own Bitt, when I install/update an app, SDWatch tells me if it can be moved to the card, or I can just launch SDMove and see if there were any I missed before installing SDWatch
• The Weather Channel: so far I haven't liked the other weather apps. I don't like this one either, actually, but I dislike it less than the others
• Traffic Cam Viewer: this app has saved me many hours in the car since I installed it. I have one client downtown, and there are essentially two ways to get home, one of which is faster but has occasional road work on it. I have traffic cams set up for those roads on my phone, and I just check before I leave the city.
• Winamp: DoubleTwist is good too, but it was claiming control from my podcast app for a lot of things, so I use Winamp instead. It'll do wireless syncing.
• Filer: for navigating the file system
• Dropin: for syncing my photos to Dropbox. I've noticed it isn't very quick, but it's better than what I had before (which was nothing)