Of course, without knowing a true budget cap or what your specific shooting style needs might be, I'll start off somewhat generically - the best cameras I feel are available in the $1,000 price range, as a kit including 1-2 basic lenses, and have the best overall combination of overall image quality, speed, accuracy, features, high ISO capability, etc.
The Sony A580 are probably right at or very near the top of the list, due to the excellent sensor shared with the Nikon D7000 and Pentax K5 - both of which are much more expensive cameras. Also worthwhile are the A560 and A550 (an older model you can find for $600ish or less).
The Pentax KR is a solid camera, chock full of features, for a very competitive price, and well worth a look - also for the slightly older model KX which is a screaming bargain at around $500.
Nikon and Canon are tougher for me on recommendations, because though I feel they certainly make competitive and excellent cameras, their better cameras tend to be a bit pricier.
The Nikon D3100 is decent, though has a few limitations like no lens motor in the camera body - still, performance is solid and features are good, and lens availability is very strong. If it can be found, a D90 might actually be a better pick - it's a better camera body and has better features. The D7000 is excellent, but a big step up in price range, closer to $2,000.
The Canon T3 seems promising - the T2 that came before it was a solid performer, if a bit slow for sports/action...the T3 is a bit of an evolution rather than a big wholesale change. The 60D is a very nice camera, great build, features, speed, high ISO - but again, you're moving up a notch on the price scale.
If you can give some idea of what styles of shooting are important to you, what price cap you'd prefer to stay under, and what features might be crucial for you, we might be able to hone the list down a little better. I'd say overall low price winner would be the Pentax KX or Sony A500 - as far as getting a nice camera for minimal money.
I'd probably have to call the Sony A580 the most performance for the best price overall - the top sensor in the biz, shared by cameras twice its price, usable high ISOs well up over 6400 (goes to 25,600), 5 frames per second burst with a 7-frame speed mode, fast and accurate focus, in-body stability system, hands-down best live view system ever, with no performance degredation or difference whether shooting with the viewfinder or LCD, tilting hi-res LCD, battery goes forever and includes a time-remaining readout, and special features like built-in automatic stacking HDR and multi-stack high ISO modes.
Sony DSLR-A68 / Sony 18-250mm / Minolta 50mm F1.7 / Tamron 150-600mm / Minolta 300mm F4 APO
Sony A6300 / 18-55mm F3.5-5.6 / 55-210mm F4-6.3 / 10-18mm F4 / 35mm F1.8 / 16mm F2.8 / FE70-200mm F4 G OSS / FE70-300mm F4.5-5.6 G OSS / via manual adapter, lots of Pentax K mount, Konica K/AR mount, and Leica M mount manual lenses