I have enthused about MyHeritage.com in previous posts, but now there is even more reason to consider a subscription if you are doing Danish research. MyHeritage.com has recently posted a significant index to Danish records from 1813 to 1923. The index to over 26 million records includes birth/baptisms, confirmations, marriages, deaths and more.
The index is not complete, and it can be difficult to find people even using the index; but any new tool in the genealogical tool-box is great help. One word of caution if you are new to Danish research, there are an awful lot of Jens and Sørens and Kirstine and others. So just because you find someone with a similar name, born on the day you great grandparent was said to be born on, does not mean it is the same person. Indexes can lead you astray as fast as they can help, so confirm you have the correct person using F.A.N. research and matching on multiple data points.