If I change my cassette to a different range do I need to change my chain? I have a Shimano 8 speed 11-34 cassette (one of those "mega range" ones).  If I change my cassette to a different one, say an 11-32, will I need to change or otherwise modify my chain?  I just got the chain replaced and now it's slipping on the old cassette.  I'm not the biggest fan of the mega range, so I wouldn't mind changing it out to something different.
Theoretically, you could shorten your chain to accommodate the smaller (largest gear) cassette.  However, I never install a new cassette unless I install a new chain as well.  Cassettes and chains tend to "wear" to one another and one can sometimes encounter difficulty if you don't.

That "could" be the issue with your new chain.  If the old chain was run past it's proper service life and damaged the cassette, no new chain is going to work well with it.  Depending how many miles/hours you put on the new chain, if you put a new cassette on your rig and leave the "new" chain, it could be fine.  

However, there are many other issues that could cause slippage.  A stiff link in the new chain if it was twisted/damaged during installation would be a prime example.