The English Standard Version (ESV)

The ESV is currently the third best selling Bible translation behind the NIV (New International Version) and KJV (King James Version).  

Like the KJV and the NIV, the ESV is an unapologetically Christian translation.  The ESV preface declares that the members of its translation team share "... a common commitment to the truth of God’s Word and to historic Christian orthodoxy..."  So, for example, in Isaiah 7:14 the ESV uses the English word "virgin" whereas some modern translations use "young woman".  The author of the book of Matthew, traditionally identified as the apostle and almost certainly a first century Jew, clearly understood this verse in Isaiah to be talking about a virgin.  The ESV is in agreement with the KJV, NIV, NLT and many other translations on this verse.

The ESV is part of a long tradition of English translations whereas the NIV was a completely new translation with no relation to those that came before.  The ESV is an update of the RSV (Revised Standard Version), which is an update of the ASV (American Standard Version), which is an update of the KJV.  So, the ESV has a familiar feel and sounds more formal and appropriate for public readings whereas the NIV is more like modern conversational English so many people may find it easier to understand.

The NIV translators put more weight on the most ancient manuscripts that have been discovered in modern times whereas the ESV tends to be more conservative in looking at the totality of ancient manuscripts along with the tradition of past English translations.  

For example, consider Romans 8:28.  

Romans 8:28 English Standard Version (ESV)

28 And we know that for those who love God all things work together for good,[a]for those who are called according to his purpose.

Footnotes:

1. Romans 8:28 Some manuscripts God works all things together for good, or God works in all things for the good

"This reading is prominent in the old English translations from Tyndale to KJV and is read by the Latin vulgate."  However, in 1831 a new Greek text was published which took advantage of newly discovered manuscripts, and "...this reading is translated by Goodspeed, RSV, NIV, and Jerusalem Bible as, 'We know that in everything God works for good with those who love him.'"  [Carroll D. Osburn, The Interpretation of Romans 8:28]

Note that the ASV translators were aware of the possible alternate translation, but they chose to put it in a footnote.  The RSV translators for some reason decided to swap the standard and alternative readings.  The ESV returns to a reading almost exactly the same as the ASV (and closely corresponding to the KJV) while once again including the alternative translation in the footnotes.

Another difference between ESV and NIV is that the ESV tries to be a more word-for-word literal translation.  Take for example 1 Timothy 3:2.  The NIV says, "Now the overseer is to be above reproach, faithful to his wife, temperate, self-controlled, respectable, hospitable, able to teach..." whereas the ESV translates the same verse as follows:

1 Timothy 3:2 English Standard Version (ESV)

2 Therefore an overseer[a] must be above reproach, the husband of one wife,[b]sober-minded, self-controlled, respectable, hospitable, able to teach,

Footnotes:

1. 1 Timothy 3:2 Or bishop; Greek episkopos; a similar term occurs in verse 1
2. 1 Timothy 3:2 Or a man of one woman; also verse 12

The NIV suggests that Paul is talking specifically about a man not cheating on his wife with another woman, but this is not the only possible interpretation of what what Paul is saying here.  He could also be talking about polygamy and/or divorce.

Anyway, I think both do a better job than the NRSV, which trying to be gender-neutral says "married only once", which makes it sound like a remarried widower could not hold the office of bishop/elder.  Furthermore, Paul clearly was writing under the assumption that a bishop/elder would be a man.  That is a fact of history whether you agree with Paul or not.

This brings us to another difference between the ESV and NIV (2011), their treatment of gender.  There was some fear that the NIV 2011 edition was going to handle gender in a politically correct fashion as part of a feminist agenda.  The publisher denies that this was ever the intent, and you can certainly see that the NIV did not make 1 Timothy 3:2 gender-neutral (as did the NRSV).  For many, though, this is a slippery slope kind of issue and so there was concern that the NIV appeared to be moving in a direction that conservatives were not comfortable with.

An example where the NIV goes gender neutral and the ESV does not is Galatians 4:7.  The ESV says "So you are no longer a slave, but a son, and if a son, then an heir through God."  The NIV makes the verse oddly inconsistent with the context, because in verses 1-6 it is talking about sons.  Verse 6 says (in the NIV), "Because you are his sons, God sent the Spirit of his Son into our hearts, the Spirit who calls out, 'Abba,[c] Father.'"  Then suddenly it switches to gender-neutral language for verse 7.  "So you are no longer a slave, but God’s child; and since you are his child, God has made you also an heir."

Notice also in verse 1 of the ESV (which comes from the KJV) it says "as long as he is a child".  That's because in common English usage the word "child" usually implies a minor.  The NIV uses the word "underage" in verse 1 instead.  Then it substitutes the word "child" for "son" in verse 7.  This could be confusing.

Of course, in the culture of the day only a male could be an heir, thus the gender-specific language is culturally correct for the day and translates Paul's words correctly.  Paul is giving an analogy from his own experience and using metaphorical terms.  He does not mean that we were literally slaves or that we are God's sons in a literal way.

It is impossible to make this passage completely gender neutral.  Even the NRSV, which goes out of its way to be as gender-neutral as possible uses the word "father" in verse 1, "...but they remain under guardians and trustees until the date set by the father."  

In at least one passage (1 Timothy 4:7) the ESV is actually more gender sensitive than the current NIV.  In this passage the NIV uses the term "wives' tales" whereas the ESV says "irreverent, silly myths."  The ESV appears to be significantly more sensitive to gender language than either the KJV or the original NIV 1984, but less gender-neutral than the NIV 2011.     [7 Places Where Gender-Inclusive Bible Translation Really Matters: Part 2]

Some people say the ESV has a Calvinist bias.  Sometimes when people say this they seem to really mean it has a conservative bias.  That's fair.  The ESV is intended to be a more conservative alternative to the gender-neutral and liberal translations.  But Calvinist?  

The ESV Study Bible has had favorable reviews from Arminians.  "When a controversial passage appears (say Hebrews 6:4-6), the ESV does a good job of pointing out the Arminian position while giving the Calvinist views as well. I have found that the ESV leans slightly Calvinist (total depravity seems to be taught from a Calvinist view but that is about it). This Bible comes with thousands of notes, great outlines, full colour maps in the Bible, and lots of extras that make it a great study Bible." [An Arminian Evaluation of Study Bibles]

If you want a study bible biased towards Arminianism there is the Fire Bible ESV Version, although it is also biased toward pentecostalism and dispensationalism.  "Even if you are not a Pentecostal (say a Wesleyan), this study Bible is useful.  The commentary is soundly conservative (for example this study Bible has only one writer of Isaiah)...  I appreciated the articles on salvation that are clearly Arminian." [Review of the ESV Fire Bible]

Of course, there are other study bibles that come in an ESV edition that are definitely Calvinist, The Reformation Study Bible and the MacArthur Study Bible.  MacArthur is also dispensationalist.  MacArthur has good notes that I often find useful and I can safely ignore the ones I disagree with.  I used to have a MacArthur Study Bible in the NKJV translation, but my eyes got to old for the small print of the notes.  However, he also has a good smartphone app which I now have and use occasionally.