Is there a reason to spread your research into multiple journals instead of just one?

There is obviously no right or wrong here, one should try to publish in the best suited journal. That said, in fields where there are several options, sticking to a single journal may look a little strange. If you publish in different (but suitable) journals, it may be looked upon as that your research is accepted by a wider set of peers. Some may perhaps also think you have a special connection to the journal etc.

So the need to publish in different journals should primarily be the focus of the journal. Some people I know enjoy the fact that they are published in widely different journals and some people may see that as your research being more widely accepted (right or wrong).

I will answer only in the prospect of making one's CV look good; note that I am a mathematician and that this certainly affects my answer, notably because in mathematics (at least from what I see in France) the impact factor is rarely considered.

The way a journal is seen can vary a lot from one person to another (for example, some journals cover several subfields but are important and selective in some subfields, less so in others). So, if you publish all your papers in the same journal, in addition to the effect described by Peter Jansson you will reduce the probability that any given person looking at you CV would think "wao, he or she published in that excellent journal Y" where Y will be A for some people, B for some else, and C for others.

In additions to the existing answers:

• CV beautifying, part 1: Publications in journals with different focus topics make you look more like an interdisciplinary person (which is usually preferred), while publishing in identically themed journals or even only one journal makes you look rather single-minded.
• CV beautifying, part 2: Excessive publishing in one journal may make you look like somebody who never tries new things and sticks to whatever is working.
• Publishing in different journals will give you a broader experience, though mostly with how publishing can be handled. There is one important exception to the latter, though: You may learn about advantages and disadvantages of the individual journals, e.g., if you only publish with journal A, you might never learn that journal B is better at organising and speeding up the review process, has a better style file, has better copy editors, etc.