1) Accuracy - their accuracy is unmatched. Seriously, reliability is the #1 reason I value Bloomberg. I've used most of their competitors and I almost always have to double/triple check primary sources if I'm going to publish the data in a high profile report, but I can rely on Bloomberg.
2) Speed - they are extremely fast to publish market news. Their reporters are very good and have a lot of primary sources and scoops, especially for companies that may not be otherwise newsworthy.
3) Excel integration - their Excel plugin is huge, it's almost like it's own program. Many of our spreadsheets are built around them. You can pretty much export every data field in the exact format you want if you know what you're doing
4) Support - they have staff available to answer questions 24/7, and their staff is extremely knowledgeable. It's the most amazing customer service I've ever experienced. Imagine you're a new analyst at an investment bank, fresh out of school, it's 1am, you've been told to put together a model and you have no idea what you're doing. You type HELP HELP in a Bloomberg terminal and they'll not only help you, but they often will make the spreadsheet for you.
All that said, their user interface is terrible (though it has its fans, and it is extremely fast once you've learned the shortcuts) and accessibility is cumbersome, especially if you're working remotely or want something fast from your desktop. But I'm still a huge fan. I don't even use it for trading, I mostly focus on equities and mergers, though they would be the first place I'd check if I needed info on fixed income or derivatives too.