1 Timothy 3 spells out some requirements for being bishops (and deacons). For example, verse 6:
Not a novice, lest being lifted up with pride he fall into the condemnation of the devil.
So it's evident that a bishop (or pastor, from episcopos, meaning "overseer") should be trained or experienced such that he is not "a novice" (from the Greek neophyton, referring to one who is newly converted).
Paul lists similar and other requirements to Titus, in Titus 1:5-9. Interestingly, most of the requirements described by Paul are related to worthiness, not intelligence or education.
There are several instances of scripture where the seemingly less-qualified men were chosen as leaders. Old Testament prophets such as David and Amos were called by God in their simplicity. (See 1 Sam. 16:1-13 and Amos 7:14-15.)
Not all prophets, pastors/bishops, and leaders have been poor or simple, however. Moses was raised by Pharoah's daughter and almost certainly had access to the royal libraries. (This is one reason I've heard for explaining how Moses knew he would be the one to deliver Israel, as mentioned in Acts 7:25. He was educated and knew the prophecies of Joseph.)
In the verses in Titus I mentioned, Paul tells Titus to "set in order ... and ordain elders." Paul also recalls that He was "ordained" in 1 Tim. 2:7 to be a teacher, preacher, and in his case, an apostle. (Jeremiah was also, see Jer. 1:5.)
We will recall that Christ found fishermen and other common laborers, invited them to follow Him, and He and ordained them to be leaders, as in John 15:16:
Ye have not chosen me, but I have chosen you, and ordained you, that ye should go and bring forth fruit, and that your fruit should remain: that whatsoever ye shall ask of the Father in my name, he may give it you.
Church leaders continued to call local leaders in a similar manner, as mentioned in Acts 14:23. Similar ordinations to positions of leadership, seemingly regardless of educational level, happened in the Old Testament from Samuel, Moses, and Isaac.
After having done a little bit of research now, I can't seem to find any real consistency in the Biblical text about the need for pastors to be educated. It's apparent that they ought to be experienced, have a sure testimony of the gospel, and meet standards for worthiness, but in ancient texts it's not easy to find any need for formal, or even informal, education: something uniquely common in our era. The Lord prepares whom He will to serve in those capacities: with or without formal education. (Though I'm sure He encourages learning and studying!)
I suppose there's an emphasis on it today because our society demands that those who instruct us be scholars and have a degree.