There are so many poetic symbols, it is difficult to know where to begin. But here are some of the more commonly used symbols in literature and poetry.
Spring is often associated with birth or rebirth, and winter is often associated with death. This dichotomy is not set in stone, of course, with an example such as death as being reborn into an afterlife or if winter symbolizing struggle, change or even birth itself as in the beginning of a new season.
Colors are significant as well. Red often denotes anger, one is "green with envy" and blue is melancholy. But again, it depends on the context. Blue could represent sky and thus symbolize the heavens or limitlessness.
Symbols can be objects, qualities, characters, relationships. In Robert Frost's "The Road Not Taken," one road symbolizes a path his life took and the other represents a path of what might have been. The "road" is frequently a euphemism for journey or life story.
Symbols cover such a broad array of figurative and referential language that you'd have to include metaphor, simile, analogy, imagery, and metonymy as functions of symbolic poetic language.
Some theorists claim that archetypes play a large role in determining what our universal character types are. Northrop Frye and Carl Jung are two such theorists.
Another symbol often used is the garden. It represents numerous things: life, growth, food, paradise and loss of innocence (Eden).
In Hamlet's "to be or not to be" speech, he symbolizes death by saying "sleep."
To sleep—perchance to dream. Ay, there's the rub.
For in that sleep of death what dreams may come,
When we have shuffled off this mortal coil, (III.i.72-74).
In other words, the rub (the catch) is whether or not there are dreams (another world, an afterlife) that come with sleep (death).
Water is used to symbolize life (among other things) because this is where life began and it is what life depends on. Water also symbolizes change because it is always flowing and/or transforming to ice and vapor. Water is also a sign of purity because it is transparent and is used to literally and figuratively (bathing and purifying-baptism) wash away dirt and impurities.