Well, for those of us in our right minds (southpaws), the Win 70s are out since they don't consider us part of their consumer base and don't make a rifle for us. I've yet to handle a Rem that I liked, though I was really close to buying a SPS Varmint lefty that I found for a really good price (the 1:12 rate of twist turned me off and broke the deal).
I really like my Savages and my accuracy results have been excellent. It will be a left-handed 111F that I take hunting this year. I've had it for almost 20 years now. I know that isn't that long for some of you guys but that's more than half my life. It began as and is currently a .243 though I have a .308 barrel for it.
My "nice" rifle though is one that no one has mentioned and that is a Browning X-bolt. It is available in just about every common cartridge (and also in some less common ones like .280 and 7 WSM), has a smooth feeding detachable magazine and a gorgeous and amazingly ergonomic walnut stock. The trigger is excellent and adjustable. The action is simple, sleek and solid. The fit and finish is as good or better than any other production rifle I've handled. It is also one of the lightest rifles I've handled. I was genuinely surprised by how light it is. I bought it earlier this year for right at $700. The only reason that it's not going with me on my mulie hunt is that I simply don't have enough rounds through it to be intimately familiar with how it shoots like my Savage. Thanks to the 7 WSM chambering and the light barrel profile I'm only comfortable shooting it about 4 rounds per hour at the range. I give the barrel ample chance to cool between shot to prolong its life.
That said, if we're honest with ourselves, you'd be hard pressed to go wrong with any of the modern rifles from the major manufacturers if your goal is put meet in the freezer. Spending more money just gets you a prettier rifle these days as far as production rifles go. The premium custom jobs might shoot slightly better but for 99% of HUNTERS that extra precision isn't needed.