What is a passage from Julius Caesar that can be related to a present day issue?

I'd suggest that Brutus's soliloquy in the beginning of
Act 2, scene 1 raises issues that most people deal with on a fairly regular basis.  In
this soliloquy, audiences see Brutus's obvious inner conflict: though he loves Caesar,
and has "no personal cause to spurn at him," Brutus is concerned by the possible
repurcussions of Caesar as a dictator. 

These lines show
Brutus's struggle to figure out the right thing to do, and it's obvious that the
situation is a difficult one for him.  Brutus has good intentions; we are aware of his
love for and loyalty to Rome, but also of his love for
Caesar. 

Ultimately, Brutus decides that crowning Caesar
will make him too dangerous and resolves to kill him before he
becomes too powerful:

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And since the
quarrel

Will bear no color for the thing he
is,

Fashion it thus: that what he is,
augmented,

Would run to these and these
extremities.

And therefore think him as a serpent's
egg

Which, hatched, would as his kind, grow
mischievous,

And kill him in the
shell.

Again, these lines
represent Brutus's inner conflict, and therefore can be applied to the present-day
issues that all humans struggle with.  While the situation (friend vs. country) may not
be one with which many of us will have to experience, the issue of the internal conflict
itself is certainly one with which all of us struggle.