Like, industrial castors? I'm having a hard time imagining that. Can you explain why a bit more?

It shouldn't effect the structural integrity of the piece but realize that its not just as simple as prying off the base board on the front- you're going to have to cut the sides (and back possibly).

I like the idea but would need more pics of the way it's structured to offer a valid opinion.

Is the dresser solid wood, or particle board? If it is particle board, I think that removing the baseboard may affect the structural integrity and that you might have trouble attaching the casters.

If it's solid wood, then maybe? But I don't think it will be a simple thing to do.

I'd have to see more of the construction underneath to know what you could do for sure. Knocking off the baseboard would change the piece dramatically, not just in stability.

If there is a solid bottom (tip it on its back and see if the bottom is solid or the drawers) you could take out the drawers and drill casters into it without taking the baseboard off at all: then the baseboard would function to hide the casters.

Otherwise, I'm sure there is something else holding it up, but I would have to see the bottom to know for sure what can be done.

I think the word you're looking for is plinth.

Depending on the height of the casters, you can put them behind the base to hide, maybe using some extra wood underneath if necessary to build the height. Otherwise, you could just attach them to the base, raising the whole thing.

51desks, that's pretty pretentious of you... a plinth is always structural, a baseboard is not. And technically, in this situation were it non-structural, it would be called molding.

Snark snark. This is funny. If there are any hesitations build a sub frame of 2x4's trimmed so that they fit just inside the skirt-baseboard-plinth-moulding-facade-structure-casing-wonderhowitholdsthatthingupey thing, and attach the casters to that. You know a square within a square. Removing the "bottom piece" would mess with the lines since the it mirrors the top of the unit. Besides it hiding the structure for the wheels it is a prime canidate for the details of the twofer paint job.
Have fun wit it!!

Not being much of a DIY'er, I've had good results placing a three-castered base under each corner of similar pieces. I think the hardware store was selling them as planter bases, but they've handled the weight stably when I move the furniture, don't damage the furniture, and can be removed in a flash.

I'm confused. Why would one want a dresser on casters?

Another thing I've tried and can recommend is just to set a piece on a thing like theskip describes making, except that it comes premade from a hardware store and is bigger, so it's visible. It's useful for temporary arrangements.

@Village, maybe OP wants to turn it into an island?

If you stop...and think....I bet she means she would like to take off the baseboard and add legs on the corners...to open up the bottom a bit.

Design*sponge had a similar idea yesterday, with legs instead of wheels http://www.designsponge.com/2011/10/before-after-curio-cabinet-redesign.html#more-118316

The plinth isn't just for looks - it's for support. And that looks like one heavy piece of furniture! I think, if you want legs or castors instead of the plinth, you would need a pair or some sort of support (like a beam) in the center as well as on each side.

But really, why? I think the plinth is needed here, both for support and to balance the design. Unless you've found some old-fashioned legs with clawfeet on them, I don't think castors would make sense at all. Unless they were hidden.

Judi here! Thanks everyone for your thoughts–
@aafilipp you are correct! Really I just want to see the floor and casters seemed like an easy way to do that while also being able to move the dresser if I please (I live alone and I like to move my furniture lots.)
I don't have pictures of the bottom, in fact I'm not even sure what it looks like which is why I feared taking off the ...plinth ..wow does that sound weird but its going into the ol' vernacular.
I'll check that out asap and if it doesn't look too out of whack I'll return with pics. Thanks again guys! ATers RULE!