Over the last 5 years of competitive racing ranging from mud runs to trail runs to road races I've changed many pairs and many brands. For a long time I was a fan of Nike then I discovered Inov-8 and ran in their shoes for a while.
A couple of years ago I've stumbled upon Altra trail running shoes and ever since then have been a big fan of them. I've now owned at least 8 pairs of various models but mostly focused on their trail line.
There are a few things I look for when looking for a new pair:
1. Weight vs Cushion - being light means swinging less weight around while a cushion size (stack height) helps in preventing shin splints (for me) and makes long runs more comfortable.
2. Zero Drop - no vertical difference between the toe and the heel, which is how our feet naturally feel standing barefoot.
3. Tread Pattern - having a rugged and somewhat pronounced pattern helps with grip on trail while adding an extra cushion on the road.
I mostly race triathlons (on and off-road) and do some trail races during in the winter months. For training I absolutely love Altra Lone Peak 3.5 because it hits all three of the above points.