Hide Google’s apps with an alternate launcher: The part of your phone that shows app icons, widgets, and contains your app list? That’s actually an app itself, and you can replace it. Two prime candidates are Go Launcher EX and LauncherPro--my preference is LauncherPro. Install either one, then tap your phone’s Home button, and you’ll see a choice of using either your default launcher or that app. Both apps allow you to hide apps from the app tray, as well as change app icons to remove any Google-y stylings.
Get alternate apps
An alternate application exists for just about every Google application offered, or installed by default, on Android phones. Some are great, some are workable, and some will make you realize the value of Google’s free-for-everyone approach. Here’s my short list of potential swap-outs:
(Note: Using the Android Market requires signing in with a Google account. That’s just unavoidable. There are work-arounds, like finding the .apk files for these apps around the web, or looking for them in Amazon’s Appstore for Android, but you could also create a Google account just for this purpose alone. It’s up to you.)
Gmail -> Yahoo Mail (or IMAP email): It works just fine if you’ve got a Yahoo Mail account, and Yahoo’s web-based interface isn’t too bad, either. Otherwise, you can use the stock “Email” app, or something better like K-9 Mail to retrieve your Gmail or personal email through the IMAP protocol, and never see advertisements.
Maps -> MapQuest: Mapquest is rather good, really, and it’s formed an interesting alliance with OpenStreetMap, which can offer deeper, community-provided results and directions. Plus it has voice-narrated turn-by-turn directions, and it also can cache the area around you for offline look-ups.
Browser -> Firefox or Opera: If you’re a desktop user of either Opera or Firefox, you’ll find their mobile apps quite nice, and easy to sync up with. If not, install both, and see which one fits you best.