Actually, all three prepositions should go with the Genitiv, but since the Genitiv is less used at least in the spoken language, it has been kind of substituted by the Dativ. Now, with 'wegen' it is 'officially' correct, so for example, in a test it is not considered anymore a mistake. This is not the case for 'trotz'. 'trotz' should be always used with Genitiv. But it seems that in the spoken language you can find it with Dativ. It still sounds pretty bad. 'statt' is usually also used with the Genitiv, but there is one exception: when you can't see the Genitiv, for example with Plural and no article: Statt Worten will ich Taten sehen.

All three are only correct with the genitive. Colloquial German tends to replace the genitive with the dative, but in a strict sense, this is wrong. If you are in a situation among educated people where you are expected to speak good German, or if you write a text, always use the genitive for these three. In daily life, copy whatever the one you're talking to is doing. A very famous article about this: http://www.spiegel.de/kultur/zwiebelfisch/zwiebelfisch-der-dativ-ist-dem-genitiv-sein-tod-a-267725.html