It's tricky tricky to assess this properly at the moment. You really need to know what a mind is, how it's distinct from - and inter-linked with - the brain, and what it does; before you can really tell who or what has one. But that hasn't been published yet. Nevertheless, I've made a working list of likely candidates at this stage, to help in the hunt for the mind. This might just be useful because we can assess the properties shared by these animals, and search for those traits not found in other animals.
We do make some inferences about the nature of others - "ahh, look at his little face! - you can tell just what he's thinking" - based upon their appearance & behaviour. This can be mawkish sentimentality - if we attribute intentions & emotions where they don't belong - but I think that we can critically appraise the nature & capacity of other animals. To some extent, anyway. I'm looking for the sort of flexible responses to the challenges posed by the world, and an appreciation of others, which suggest that mental processes are going on. Let's give it a try:
It seems reasonable to accept that we share so many important traits and abilities with the great apes, and I'm sure that includes consciousness. But what about other mammals? People who spend time with dolphins cherish their personalities and awareness. Dogs and some other pack animals seem conscious - sensitive to the intentions and emotions of others. There seem to be plenty of mammals whose behaviour can't be wholly understood as reflex actions and instincts.
It's not yet clear whether we can say that all mammals have mental activity though ((But when you watch youngsters "playing", don't you feel that there is awareness & spontaneity in their behaviour, which isn't there in the behaviour of, say, a stick insect, scorpion, snake or starfish?)), but it seems reasonable to say that consciousness - mental states & activity - is found in a number of mammalian orders. And not just those who use language, Ludwig.
Other good candidates include some species of birds, especially the more intelligent ones, such as corvids (crows & magpies) and parrots. I'm not sure about the rest yet.
Perhaps this might surprise, but some biologists consider that cephalopods (such as octopuses and cuttlefish) are very intelligent, and also have some form of awareness or consciousness. They seem to behave differently from most other invertebrates - they do not just act instinctively, or react by reflex. They display an adaptability, ingenuity and understanding that indicates awareness of their environment, themselves and others. I interpret this as evidence that they experience mental events and states.
This has to be a provisional list - and I've erred on the side of caution - until a convincing description of the mind is published. Nevertheless, if we can tentatively accept this list, then this exercise suggests something: that consciousness has arisen independently a number of times. The common ancestor of those phyla (molluscs and chordates) would have been early (~550-600 million years ago), and a relatively small & simple multi-cellular organism - because it had to directly transport some of its nutrients between cells (see previous posts for explanation, here and here). It seems unlikely that such a creature was conscious; but if it was - then why did so many other molluscs (and simpler chordates) subsequently relinquish this trait? Therefore, it seems reasonable to believe that mental activity has arisen a number of times.
Perhaps this is encouraging, no? If consciousness can start more than once on this planet, then perhaps it isn't so astronomically unlikely, and maybe it isn't quite so exotic as some thinkers would have us believe: it isn't a new unknown type of force, quantum effects on specific proteins, or a multi-dimensional crystal. Whatevs.
Well, it's encouraged me to carry on with my work on a simpler biological account of the phenomena of the mind and its relation to the brain.
Blog Supplemental: it's just struck me that some might think that I've just identified the most intelligent species, and that the highest common factor between these species is relatively large brains. Therefore, it might be thought that this approach suggests that consciousness & mental events begin once the brain gets large enough and it crosses a threshold. That the mind is an emergent property of a large brain. You may draw that conclusion if you like.
However, I have reason to think that increasing the size and complexity of the brain, the number of neurons and connections, are not the keys to making the mind. They're necessary, but they're not sufficient. Apparent intelligence isn't sufficient for us to credit the demonstrator with mental processes either - consider the computer that can give questions to answers better than any human.
Please remember: the mind is distinct from the brain, and the brain isn't a computer.