I'm not going to go in depth here, but I want to give an overview of some of the tools I use and recommend. I will start with free tools and work my way up.
YouVersion (also known simply as "The Bible App") Free:
OliveTree (Desktop and Mobile):
A fantastic free app, with the ability to purchase additional resources. Denny Burk from SBTS did an excellent write up on OliveTree recently. I have not used it much, so please check out his write-up for more info.
Lumina Bible Study Tool (Website) Free:
This is the app I use the most on my phone. It is exactly what it sounds like. It has the text of the ESV Bible (in the same font that Crossway uses in their physical Bibles) combined with the ESV Study Bible notes and resources. A new version coming soon will allow you to sync your personal notes between the Web app and the iOS app.
HCSB Study Bible (Website Free and App $4.99):
The Website is a fantastic free resource with access to the HCSB Study Bible notes and a choice of several English translations. I was terribly disappointed with the iOS app. I loved the features, but it didn't fit the iPhone 5/5s screen size instead putting black space at the top and the bottom. I e-mailed Lifeway to inquire and was told that Olive Tree developed that app for them, Olive Tree was purchased by (competitor and NIV translator) Harper Collins which cancelled their agreement with them. In short, the app isn't going to be updated, which is a bummer because I paid $9.99 for the app and Lifeway did not offer a refund in my interaction. They did mention that they would be looking into creating new apps in the future, and my reply asking if those "future" apps would be free upgrades for those who purchased the HCSB Study Bible app, was not answered.
Now For the Big Guns:
For a full fledged Desktop solution with access to huge libraries (potentially costing huge amounts of money) as well as many integrated tools, features, search tools, markup tools...more stuff that I can possibly list here, check out Logos, Accordance or BibleWorks.
I chose Accordance, but your mileage may vary. I ruled out BibleWorks right away due to the lack of a Mac version. Accordance was on Mac first, and has the reputation of being the most polished tool for Mac (although they now have a Windows version and Logos now has a Mac version). I would advice scouring through the features, library packages and pricing just as I did before making a decision. This is an expensive decision.