The official Tumblr app for iPhone isn't bad at all, it'll do for most users, also the UI of the app is great. But if you want to take your Tumblr experience to another level on your iPhone, as well as your iPad, TumbleOn is the way to go.
This brilliant app makes browsing Tumblr a lot more of a better experience and is definitely targeted at the power users who run multiple blogs, follow hundreds of people and reblog tons of pictures.
The app is mainly made for photo Tumblr blogs so if you follow blogs which are mainly text based this may not be the best.
The photo stream viewer is awesome and makes photo browsing a whole lot better. Multiple photos can be shown on the screen at once and you can adjust this to either 1 row of photos, or 5. In the picture you see above it is set to 3, but you can already see how many photos fit on the screen.
If you have an iPhone 4S and an iPad you'll be pleased to know high res picture are supported so that screen will be utilised a lot better.
The "Explore" tab is brilliant and brings the desktop browser of exploring on Tumblr, to your iPhone and iPad. There is a "Blog Lookup" feature which will let you easily find your favourite blogs, even ones which you aren't following.
One of the most unique features has to be the "Groups" tab. You can create groups and put blogs in those groups. So you can easily organise blogs into categories, for example, architecture, cars, girls, photography...etc. It's a brilliant feature and I don't know why Tumblr haven't actually implemented this kind of feature on their site.
The iPhone version of the app is currently FREE until 13th of July, so get it quick! The iPad version though is £1.49.