I think that there will always be a place for the HDD, because I don't think that SSD prices will ever come down to the same price per terabyte as rotating platters. So HDDs will continue to exist for large-volume storage where lower speed is acceptable. Like backups, as an extreme example. My SSD gets backed up to removable hard drives.
Servers are already using SSDs. For huge databases that serve massive numbers of users in parallel (Web pages, Wikipedia, Oracle databases), the huge advantage in read speed and in IOs per second makes them well worth the expense. With a large amount of expensive SSD storage, one server can do the work of several that use HDDs.
For DVRs, I don't ever expect to see SSDs. Read and write speed is simply not important for these devices. The transfer speeds for 3-D Blu-ray are well within the range of SSDs. Flash storage is used in bulk for portable devices because they are portable, but a DVR sits in one place and can afford the power budget for the drive.