Everybody likes free stuff - unless it's garbage you have to dispose of. This is no different with getting psychic readings, especially if they can be communicated conveniently online. However, there are a few things you should pay attention to.
To quote Heinlein: "There ain't no such thing as a free lunch." This means that even if you get something for free, somebody somewhere had to invest time and energy in it, and getting it for free will have repercussions in the long run even for you.
Unfortunately, the demand for free online psychic readings outstrips the supply. To address this problem, people try to do more with less, and the end result is that these readings get automated. Such readings are made by software programs that choose a combination from a number of preset answers. There is nothing psychic about such mechanized readings, but they still have a purpose if they provide you with some entertainment (if that is what you're looking for).
The bad thing is if you don't realize that you are not getting a personalized reading from an actual psychic. A skillful psychic can notice many things about you that don't fit into large stereotypes, and can help communicate that insight in a way for it to make clear sense to you.
In many cases you get what you pay for (just make sure you don't get ripped off). In rare cases you might even find an offer for a personalized and free psychic reading by a nice person who wishes to demonstrate his or her skills or to do a favor - go for it!