The best option, and one which I use myself, is two fold. I've done this for a couple years now, and while at times it is tedious, it is the only way I actually feel safe about my LARGE photography library (~40,000 RAW photos, averaging around 23mb each) as well as my growing library of edited photos, photos sized for web publishing, photos sized for various print sizes, etc. My total library, including Lightroom catalogs, is a little over 1 Tb.
My primary backup source is a NetGear ReadyNAS NVX. This is a Network Attached Storage device, or NAS. It holds four hard drives (platters, not SSD), and currently I have all four slots filled with 2Tb drives (8Tb raw space, some of which is allocated to parity.) This device is extremely fast, 75mb/s transfer rate on average, with a burst around 100mb/s. It is a full RAID device, so if one of the drives fails, I can swap it out and replace it with another and the system will rebuild the data that would have otherwise been lost automatically. The ReadyNAS is also an X-RAID device, so you can automatically and dynamically expand your volume onto more drives or larger drives without taking it offline (which is simply amazing.)
My secondary backup is LTH-type BluRay discs. These are high quality discs designed to be written to once and stored for a LONG time. Lab tests indicate these puppies will have at least a 10 year shelf life, potentially much longer. I buy Verbatim discs, as they are a trusted brand with a good reputation. I use these to periodically burn a copy of my library for off-site storage (which in my case is generally my car. ;P)
From a strategy standpoint, I actually have three levels of backup. I use Acronis True Image as my initial "active" backup. All of my photography locations, my RAW import folders, my work folders with all my TIFFs, and my Lightroom catalog, are all watched by Acronis NonStop backup. This actively watches for changes, and backs up each and every one. I have a full moment by moment history of every save I ever make, going back for months.
A couple times a month, I'll copy my entire library, RAW import folders, work folders, and catalog, to my NAS. I keep two copies, the current and the last, and delete anything older than that. (I don't have a lot of choice, as two backup copies is already over 2Tb of space).
Every month or so, I will burn the most recent copy of my full backup on the NAS to LTH BD-R. This is the tedious, time consuming part, as I have to build each disc, burn it, label it, and store the discs off site. And somewhat costly...I need two stacks of 25Gb LTH dics which cost about $50, so I try to do this as infrequently as I feel safe doing it. But it IS the long-term backup, something I expect to last a good portion of my life, if not beyond.
Anyway, this is the complex solution. If you wish to have a simple solution, I would recommend getting a NAS of some kind (ReadyNAS is VERY good, and X-RAID is the best RAID system there is), and simply schedule a small script to back up your library on a regular basis. Keep a short history, maybe two or three backup copies, and leave it at that. Having a RAID device, unless something actively fries or otherwise destroys the NAS device itself, your data is going to be far more reliable than even on a couple external drives.