Which cameras do you prefer to use:Mirrorless, DSLR or Smartphone and Why?

Mirrorless because they can be adapted to use a huge variety of lenses from nearly any brand of 35mm-format lens manufacturer. Mirrorless cameras are smaller, they've got an EVF which shows the focusing point and the exposure before actually taking the shot. Many have in-body image stabilization (IBIS) which provides 5-axis stabilization up to about 5.5 stops. No DSLR (except for Pentax) has IBIS. Focusing speed and accuracy is not an issue just as long as you're using the top-of-the-line models like the Sony A9 - otherwise the AF speed/accuracy sucks.

I like DSLRs because of the OVF works better in a lot situations without any lag, and a DSLR will usually have faster AF speeds.

In the end, which one I'll use depends upon the needs determined by the shoot. With the introduction of the Sony A9, it really looks like DSLRs have one foot in the grave.

You forgot to mention 'compact' cameras. Many people still use compacts (handy for the pocket or handbag)as more versatile alternatives to the cameras in smartphones.

DSLR cameras have an approximate shutter curtain life.

I think the mirrorless cameras have a shutter too.

Right now a full size sensor mirrorless camera body is too expensive for me right now.

DSLR. The reason why is because it's the only one that I have ... and I don't have the financial werewithal to be able to purchase anything else.

Many newer mirrorless models have electronic viewfinders in addition to the preview screen and crush the DSLRs in all specs as they have become the evolution of the older DSLRs.  Having an electronic viewfinder is better since it shows you the exact exposure of the sensor rather than just an optical view through the lens.   Otherwise a good camera phone is useful in a pinch.  The newer flagship phones often take better fixed lens pictures than most of the older DSLR's.  You can find many side by side tests online that easily prove the point. 

Like Keerock, I moved from 35mm to a DSLR, which I carry when I know I'll need a camera.

Otherwise, I carry an advanced compact (Canon G11) at all times. I regard my phone camera as worse than useless.

DSLR.

I learned to shoot pictures with film using an SLR. It was just but natural for me to slide into digital using my old lenses. Up to now, I find myself holding up a mirrorless or point-and-shoot to my eye when shooting. Worse, I tend to do that too when friends ask me to take pictures with their phones.

I used to carry my camera along with all the peripherals but today smartphones made that kind of pointless

DSLR over mirrorless mainly due to battery life. My trips take me in to remote areas for a few weeks where no power is available. Taking extra electronics junk (solar charger systems) requires too much attention and is prone to failure in the field. Much easier to carry an extra battery. Also, I like an optical viewfinder. My pocket camera is a 1" sensor type which can be used in manual exposure mode for both stills and video.

The DSLR takes a much better photo and you have more lighting options including manual settings.