Tabbed browsing is a good place to start. This is less of an issue on the small screen of an iPhone/iPod touch, but on the iPad, I really miss having real tabs that I can easily and quickly switch between. Safari doesn't have that, but iCab does.
Found a file that you want to download? Safari might let you view it, but iCab will let you download it. You can then move it to your Mac using iTunes file sharing (why can't Safari do that?) or upload it to your Dropbox (something Safari will probably never offer). Do you want to save the current webpage as a "web archive" file? iCab can do that, too.
Want to upload an image from your photo library to a website? Safari has no idea what you're talking about or why you'd ever want to do such a thing. iCab, on the other hand, is happy to help.
Need to add a bookmark? Safari can do that. Want to edit that bookmark before you save it? Safari can't do that, but iCab can. Web filters? Safari: no, iCab: yes. Customized search engines that you can switch between easily? Safari: no, iCab: yes. Safari can save forms and password data, but iCab will let you assign password protection for that information.
Want to be able to let other people use your iPad without accessing your browsing information? So sorry, Safari users, but iCab has a Guest Mode that even allows them their own bookmarks and search engines. How about private browsing? iCab can do that.
Some website blocking you based on your browser's user agent? iCab can easily change between iPhone, iPad or any of over a dozen other browser IDs. iCab will also let you configure 3- and 4-finger gestures to switch tabs, navigate history, increase or decrease font size or several other actions.
iCab comes with over 20 modules that let you do everything from adding the current page to Pinboard to opening the current site in Google Reader, Evernote, GoodReader, Instapaper and more. iCab also has full-screen mode and the ability to open links in different tabs; you can even tell iCab whether you want them to be background or foreground tabs. Reading a webpage and find an interesting link? Tap it, and have it load in the background while you continue to read the current page uninterrupted. iCab can also have "links to the same domain" respond differently than "links to other domains" if you wish.
Still not convinced? How about being able to disable images or turn Google Mobilizer on for all sites by default? How about an "offline mode" so that you can even browse cached sites when you aren't connected to the internet? There's even a "QuickStarter" page where you can enter your most frequently accessed websites. Tell iCab to show the QuickStarter when you open a new tab, and tap where you want to go. iCab will even cache a thumbnail of the sites to give you visual cues to find sites you want quickly.
Think of iCab Mobile as "Safari Pro" -- it does everything that Safari can do, plus a whole lot more. About the only drawback is that Apple does not give you any way to specify a different default browser on iOS, so any links that you open from Mail, Twitter, etc. will automatically open in Safari. Most of the time that doesn't bother me, and if it does, I just tap the "Open in iCab" bookmarklet I have installed in Safari. Some applications, such as myPhoneDesktop, are starting to include support for opening links in iCab instead of Safari, which is a trend I hope will continue.
If you do a lot of web browsing on the iPad, you owe it to yourself to spend $2 to see how much better browsing can be with iCab. I bet you'll find yourself wondering why Apple hasn't added a lot of these features to Safari. Maybe someday Apple will improve on Safari, but I don't ever expect to see integrated Dropbox support. That feature alone is worth $2 to me.