There are heaps of bugs to catch (namely 40). This list will help you
to track them all down :)
Keep in mind that some bugs can be found in more than one season.

Season: All season | Spring | Summer | Autumn | Winter | Check List

All-season bugs:
Pill Bug
All year
All year
All year
All day
All day
All day
Attracted to candy and turnips
in trees
under rocks
80 Bells
4,500 Bells
250 Bells