Parish registers online
Over 1 million Derbyshire baptisms and marriages are included in the IGI at FamilySearch but not all parishes are included (you can see the coverage here). FamilySearch have also recently added nearly 1.5 million baptism, marriage, and burial records - there will inevitably be some overlap with the IGI records.
Findmypast has nearly 1 million births, three-quarters of a million marriages, and nearly half a million deaths from 1837 onwards which have been indexed from the local register office records by Derbyshire Family History, however there's litle information in these records that you wouldn't find in the GRO indexes (and they're definitely births and deaths, not baptisms and burials as the search results imply).
Findmypast also has transcriptions of nearly 82,000 burial entries from the National Burial Index.
The volunteers of FreeREG have transcribed some of the registers for every Derbyshire parish, although the extent coverage varies considerably. The main focus has been on marriages; much smaller numbers of baptisms and burials have been transcribed.
The Derbyshire Marriage Index compiled by Sue Brown includes over 75,000 marriages between 1538-1837; the Wirksworth website has 88,000 parish register entries for Wirksworth and Middleton from 1608-1899 as well as hundreds of thousands of other records for Derbyshire.
Births, marriages and deaths
Bakewell 1725, 1740-2, 1754-1812, Barlborough 1792, Boylestone c1600, Breadsall 1701, Chesterfield (pt) 1821, Clowne 1801, Crich 1811, 1821, Darley 1696, Doveridge 1710-51, 1821, Eckington 1801, 1821, Findern 1811, Hathersage 1729, 1814, Hope 1811, Littleover 1811, Mackworth 1821, Marton on Dove 1671-1746, Melbourne 1695, Mickleover 1811, 1821, Morley 1774, 1787, 1801, 1811, Ockbrook 1821, Smalley 1801, Smisby 1830, South Normanton 1821, Tibshelf 1696, 1698, Ticknall 1821,, Whittington 1831
Key Derbyshire resources
Derbyshire Record Office based in Matlock opens 6 days a week; to access original documents you will need a CARN card, but you can get one free on arrival provided you bring the right documentation. Apart from parish registers, key holdings include electoral registers from 1832-1999, prisoner records (there is an online index covering the period 1729-1913), and some wills from 1858-1928 (again there is an online index). Wills prior to 1858 are held by Lichfield Record Office (Derbyshire is in the diocese of Lichfield), and there is a free online name index.
Derbyshire Record Office has a database of Poor Law Removal Orders from 1710-1865, and whilst it can not be searched online at present, staff at the record office will carry out a free search on request.
Debryshire Family History Society currently meets regularly in Derby, Glossop, and South Normanton. They have an online index to burials between 1855-1904 at Nottingham Road Cemetery, which was one of the two main cemeteries in Derby at that time; the index is free to search, but there is a charge of £5 for a scan of the burial register entry and a scan of the grave record showing the names of others buried in the same grave.
Chesterfield and District Family History Society, which meets in Chesterfield, covers the 65 parishes that formed part of Scarsdale Hundred. There is an online surname index to tens of thousands of records at Chesterfield Local Studies Library (the index was created by volunteers from the society).