No, bugs are not kosher. If you see a bug on your plate, make sure to remove it. In fact, before Jews eat lettuce or other produce known to be infested with bugs, they check it carefully to be sure that it is bug free.

That said, even though bugs are not kosher for consumption, Judaism has some complimentary things to say about creepy crawlies. The sages tell us that even if the Torah would not forbid thievery, we would know not to steal by observing the ants, who are particular not to take even a kernel of grain that has already been taken by a fellow ant.1

Also note that some species of locusts are allowed by the Torah, and they are still enjoyed by certain communities, who have a tradition regarding the identify of these locusts. Most Jews, however, do not eat locusts at all. Read more about that here.