10 Good men not made bishops

1. John Knox c1514-1572 (... Dudley, who saw Knox as a useful political tool, offered him the bishopric of Rochester. Knox refused, and he returned to Newcastle ....)

2. Bernard Gilpin 1517-1583 (... When the Roman Catholic bishop was deprived in 1560 he was offered the see of Carlisle; but he declined this honour ....)

3. Thomas Sampson c 1517-1589 (... he wrote again, signifying that a bishopric had been offered him, but he had refused to accept it; for which, he desired Peter Martyr not to censure him, till he became acquainted with the whole matter. He rejoiced that Parkhurst was made Bishop of Norwich. And Norwich, it seems, was the bishopric offered to him. This illustrious divine, therefore, refused the offered preferment, because he was thoroughly dissatisfied with the episcopal office, the popish habits, and the superstitious ceremonies .... see here)
4. John Rainolds 1549-1607 (... So contented was Rainolds himself with his position, and so ‘temperate,’ according to Wood, ‘were his affections,’ that he declined a bishopric which was offered to him by Queen Elizabeth .... see here)

5. Daniel Cawdry 1588-1664 (... At the Restoration he was recommended to Lord Clarendon for a bishopric. Instead he refused to submit to the Acts of Uniformity 1662, and was ejected ...)
6. Edmund Calamy 1600-1666 (... He was assiduous in promoting the return of Charles II, travelling to the Netherlands as one of the negotiators. After the Restoration in 1660 he was offered the bishopric of Coventry and Lichfield, but declined it ....)

7. Robert Baillie 1602-1662 (... He was, by Lauderdale’s interest, made Principal of the College of Glasgow, upon the removal of Mr Patrick Gillespie. About which time, it is commonly said that he had a bishopric offered him, but that he refused it ... see here)

8. Richard Baxter 1615-1691 ( ... He had been made a king's chaplain, and was offered the Bishopric of Hereford, but he could not accept the offer without assenting to things as they were. After his refusal, he was not allowed, even before the passing of the Act of Uniformity, to be a curate in Kidderminster ...)

9. Joseph Hill 1625–1707 (do not confuse with Joseph Hill 1667-1739 ... In London he went to Charles, who rewarded him for his pamphlet with a sinecure, and tried the offer of a bishopric if he conformed ....)

10. John Stott (... There was talk of his becoming Bishop of Manchester, but the Dean and Chapter took fright and nothing came of it ... see here)
Quotations from Wikipedia where not otherwise indicated)