Mind precedes all mental states.
Mind is their chief; they are all mind-wrought. 
If with an impure mind a person speaks or acts, 
suffering follows him like the wheel that follows the foot of the ox.

Mind precedes all mental states. 
Mind is their chief; they are all mind-wrought. 
If with a pure mind a person speaks or acts, 
happiness follows him like his never-departing shadow. 
Dhammapada v. 1, 2

The mind is hard to check. It is swift and wanders at will.
To control it is good. A controlled mind is conducive to happiness.
The mind is very hard to perceive, extremely subtle and wanders at will.
Let the wise person guard it; a guarded mind is conducive to happiness.
Dhammapada v. 35, 36

A straightforward mind is the site of enlightenment.
Vimalakirti Sutra

It is a man's own mind, not his enemy or foe, that lures him to evil ways.

Consciousness will always be present, though a particular consciousness may cease. For example, the particular tactile
consciousness that is present within this human body will cease when the body comes to an end. Likewise, consciousnesses that are influenced by ignorance, by anger or by attachment, these too will cease. But the basic, ultimate, innermost subtle consciousness will always remain. It has no beginning, and it will have not end.
Answers: Discussions with Western Buddhists

Question: What is the nature of the mindstream that reincarnates from lifetime to lifetime?
Dalai Lama: ...If one understands the term "soul" as a continuum of individuality from moment to moment, from lifetime to lifetime, then one can say that Buddhism also accepts a concept of soul; there is a kind of continuum of consciousness. From that point of view, the debate on whether or not there is a soul becomes strictly semantic. However, in the Buddhist doctrine of selflessness, or "no soul" theory, the understanding is that there is no eternal, unchanging, abiding, permanent self called "soul." That is what is being denied in Buddhism.
Buddhism does not deny the continuum of consciousness. Because of this, we find some Tibetan scholars, such as the Sakya master Rendawa, who accept that there is such a thing as self or soul, the "kangsak ki dak" (Tib. gang zag gi bdag). However, the same word, the "kangsak ki dak," the self, or person, or personal self, or identity, is at the same time denied by many other scholars.
We find diverse opinions, even among Buddhist scholars, as to what exactly the nature of self is, what exactly that thing or entity is that continues from one moment to the next moment, from one lifetime to the next lifetime. Some try to locate it within the aggregates, the composite of body and mind. Some explain it in terms of a designation based on the body and mind composite, and so on.... One of the divisions of [the "Mind-Only"] school maintains there is a special continuum of consciousness called alayavijnana which is the fundamental consciousness.
Healing Anger: The Power of Patience from a Buddhist Perspective

Patricia Churchland: But do you think that there is something, I am not sure what to call it -- a kind of awareness that can exist independently of the brain? For example, something that survives death?
Dalai Lama: Generally speaking, awareness, in the sense of our familiar, day-to-day mental processes, does not exist apart from or independent of the brain, according to the Buddhist view. But Buddhism holds that the cause of this awareness is to be found in a preceding continuum of awareness, and that is why one speaks of a stream of awareness from one life to another. Whence does this awareness arise initially? It must arise fundamentally not from a physical base but from a preceding continuum of awareness.
The continuum of awareness that conjoins with the fetus does not depend upon the brain. There are some documented cases of advanced practitioners whose bodies, after death, escape what happens to everyone else and do not decompose for some time -- for two or three weeks or even longer. The awareness that finally leaves their body is a primordial awareness that is not dependent upon the body. There have been many accounts in the past of advanced practitioners remaining in meditation in this subtle state of consciousness when they died, and decomposition of their body was postponed although the body remained at room temperature.
Consciousness at the Crossroads: Conversations with the Dalai Lama on Brain Science and Buddhism

Question: What is the role that consciousness plays in the process of reincarnation?
Answer: In general, there are different levels of consciousness. The more rough, or gross, levels of consciousness are very heavily dependent upon the physical, or material, sphere. Since one's own physical aggregate (the body) changes from birth to birth, so too do these gross levels of consciousness. The more subtle the level of consciousness, however, the more independent of the physical sphere, and hence the more likely that it will remain from one life to the next. But in general, whether more subtle or more gross, all levels of consciousness are of the same nature.
Answers: Discussions with Western Buddhists

If the first true fact is that life in general is not easy, we should certainly not expect that seeing the nature of our mind will be simple. The actual nature of mind, on any level, is not very obvious. Even to identify and recognize correctly what is mind is extremely difficult. Just to start to try to see it, we need strong motivation. We need to be clear about why we would like to see the nature of our mind.
The Gelug/Kagyu tradition of Mahamudra

The basis on which Buddhist[s] accept the concept of rebirth is principally the continuity of consciousness . . . If you trace our present mind or consciousness back, then you will find that you are tracing the origin of the continuity of mind into an infinite dimension; it is, as you will see, beginningless.
Therefore there must be successive rebirths that allow that continuum of mind to be there.