When the dessert is cake and is one of the doubtful categories of Pas ha'Ba b'Kisnin (see Insights 42:1), it is a doubt if its blessing is covered by the ha'Motzi at the beginning of the meal, and therefore one does not make a blessing. If the dessert fulfills all three conditions of Pas ha'Ba b'Kisnin, then it is definitely not bread and requires a blessing -- but this is only if it is being eaten for its good taste alone. If it is being eaten to satisfy one's hunger and to fill him up, it is considered part of the meal and one does not recite a blessing. This is what has been written in the name of Rav Sheinberg (see, for example, Sefer v'Zos ha'Berachah, p. 74).

As far as non-grain desserts, such as fruit, ice cream, chocolate, etc., the Halachos are different and there are differing opinions and we recommend that you ask your local rabbinical authority.