I'd say that dogs experience the equivalent of what we call love, like another has suggested this may be a stronger emotion than love. This is based off two pieces of evidence.
- I live away from home for extended periods of time, my parents look after my dog my than myself. However when I go home I get crash tackled by my dog then muredered with licks and my ears are bombarded by the noises she makes. Similarly, when I love my mum has told me that she waits at the front door all day except for food for about a week after ive left again. The first few times were especially bad, she destroyed my couch, the garden, my bed, the doors in my house and the carpet on he stairs in what my parents describe as a month long fit of insanity, they said they had no idea what they were going to do with her.
- the second piece is a story of one of the blokes from an EOD unit based in Darwin. During a patrol in Afghan this EOD unit was hit with an IED, in this unit was a bomb detection dog and it's handler. The initial blast injured the handler but didn't injure the dog, later, despite medical care the handler passed away from his injuries. Two days later the dog died too, with no injuries or internal tissue damage found.
In short, yes, I believe dogs feel incredible bonds with their owners, whether it's technically love I can't really say for certain.