[demonat0r]

How come no reaction occurs?
I thought it would be I2 + 2Cl- ~~> 2I- + Cl2

also, a silver wire is placed in a solution of CuCl2.
again, i thought it would be 2Ag + Cu2+ ~~> 2Ag+ + Cu
but my book says no reaction.

why don't these two scenarios make a chemical reaction?

[lancenti]

The answer to both questions can be found by looking at the Reduction Potentials of the four.

Alternatively, for the I₂/Cl₂ question, you can look at it in terms of electronegativity. Since Chlorine is more electronegative, it is more likely to take a negative charge than Iodine is.

[Borek]

The answer to both questions can be found by looking at the Reduction Potentials of the four.

Or - in even simpler form - reactivity series. Which is based on redox potentials, so it basically boils down to the same.

[Arkcon]

You should have been able to guess the reactivity series for the second one at least.  Silver is found native, it tarnishes a bit, but doesn't corrode -- that is react with the atmosphere and form molecular compounds, that crumble away.  But copper does.  Would you take a solution of sodium chloride, stir it with a rod of pure platinum, and expect to get sodium metal, and a solution of platinic chloride?  That's a wild exaggeration, but you should make some guesses when jewelery class metals enter the discussion.