The rubber of the ping pong rackets has been subjected to a great number of tests during official competitions over the years, which resulted in banning quite of few types. Since 1986, the ITTF will only accept rubbers that are colored in either black or red for paddles used in official competitions. This resolution was reached mostly because other colors seemed to make the effects of different strikes of the ball rather hard to see, especially when players used rubbers that had the same color as the ping pong ball. Moreover, if you want to be sure that the rubber you are using for your ping pong rackets is legit, you need to check that the ITTF logo is inscribed on it.
As far as the physical properties of the rubber are concerned, there are three types that are approved by the ITTF: the ones with thick sponge, the rubbers with pimples outwards and the rubbers with pimples inwards, each of them designed for a different play style, with its own advantages and faults. For example, if you tend to base your game mostly around offense, the best choice would be using ping pong rackets with thick sponge rubber, in order to apply more force to your strikes.
The rubbers using outwards pointing pimples come in two types, the ones with long pimples and the ones with small pimples. However, the rules of ITTF clearly state that the density of the pimples should be between ten and thirty per square centimeter, so keep this in mind when you are choosing your ping pong rackets. At the same time, the rubber should not be thicker than two millimeters. According to your game style, you should use a rubber with long outward pimples if you are the kind of player that is good at blocking and counter attacking and rubber with smaller pimples if you game revolves mostly around defense.
If you are aiming to purchase ping pong rackets with rubber that will allow you a wide variety of strikes, your best bet would be the ones with inwards pimples. The rules that apply to this type of rubber are the same as the ones for outward pointing pimples.
One thing that the ITTF is taking very seriously when it comes to the ping pong rackets is whether the outer and inner surface of the rubber has been treated with chemicals or not. The way to verify this is by checking the friction level of the rubber. If it does not meet the minimal requirement, the rubber will be banned from the competition. This decision will mostly affect players that prefer to use longer pimples on the rubber of their ping pong rackets as well, but the proposition for this rule came from the players themselves.
Modifications that have occurred to the color or the surface of the rubber because of extended use will be approved, unless they will cause major changes in the trajectory of the ball.
If you want to be sure that you will purchase ping pong rackets that are approved by the ITTF and that you will be able to use in official tournaments, it is a good idea that you check the list of approved brands constantly.