Is it worth it to try a really low offer on a property?

There is nothing wrong with trying a real low-ball as long as you are reasonable in your expectations. 

For one thing, you certainly shouldn't be surprised if they are not willing to accept it.  For that matter, you should be prepared for them to be offended and simply choose not to even send back a counter-offer. 

Just to be clear, I'm not talking about a normal offer coming in below list price to leave room for negotiation.  Nobody wants to pay full price if they can help it and a little bit of haggling is to be expected, but no seller wants to sell below fair market value either.

Properties typically sell within 5% of list price at the time of the offer.  (Obviously, competing offers changes the situation completely)  So if you're 20% below the list price, it's most likely going to be a tough sell.  Even if you honestly think the property is only worth your lower price, the seller obviously has different thoughts on the matter.  You can still try, nonetheless, if you have an agent who is willing to do it.

If you're looking for an investment property, it might be what you need to do in order to make the deal work for your long term goals.  I always advise investor clients to keep emotion out of it and offer only what they are comfortable with for their purposes.

A low offer is a bit riskier if you're looking for a personal home and the house you're offering on is "the one", since you might well offend them to the point where they simply won't be very cooperative with you, even if you bring in an offer closer to what they are looking for.  And as a side note, if you can't afford the house without the much lower price, you might want to re-visit your needs and wants to bring them in line with your buying power.

In any case, talk to your real estate agent and get their opinion.  Sometimes really low offers will work out.  And often they won't, so it's just a matter of managing expectations.