As Bit points out, this is a very context specific question! If I had the money I'd probably own half a dozen libraries to cover all the bases, but alas I don't.
I use the 8Dio Adagio/Adagietto/Agitato series a lot, especially for smaller string sections. I absolutely love their dynamic bowing patches, although they can be very frustrating to use. I did take advantage of the cross-grade to Anthology, but I'm so accustomed to the previous versions that I haven't really given it a fair shake.
For larger sections I use Cinematic Scoring Strings, and they just work. They don't have quite as many articulations, but sometimes that's a good thing. And they sound absolutely gorgeous, and they are really easy to learn. There is just nothing negative to say about this library.
Recently I picked up Alex's Cinematic Studio Strings and they do give 8Dio a run for their money. They are far easier to use, but sometimes I really do want the microscopic control I get with 8Dio.
For rock and pop productions I still use Kirk Hunter's Rock and Pop Strings, or Native Instruments Session Strings. I have the basic version, and quoting Bit again, for simple pop arrangements both work quite well, you can get a little more detail with the KH library, and it is appropriately aggressive.
I started with KH Diamond, later upgrading to his Concert Strings 2. I no longer use them, although they are still on the hard disk because every once in a while I think they might be just the thing. I think my tastes have changed, because I always seem to gravitate towards my other libraries for strings, brass, and winds.
Depending on what you are after I should also mention the ensemble type libraries - I have Albion One and Orchestral Essentials 1 & 2. I struggle a little bit with using them because my brain just doesn't work that quickly, and i need to think in terms of sections - a shortcoming on my part I'm pretty sure. They do sound gorgeous though.
Needless to say, I've left out LASS, East West, Orchestral Tools, Cinesamples, and others which I don't own. They all have their good points.
Some might say it is a problem to have so many choices, I'm not sure it isn't a good thing<G>!