I wasn't sure how old a ticket was on my record, so, at one point when I was getting quotes I just told them I had a ticket or something a few years back but didn't know exactly when. That way they know they need to check my record. Most of the big companies can do it right at the time of the quote, they ask for you DL# and SS# and run a credit and driving check right then.
If they denied your coverage because they didn't check your record and claim you lied about it you could possibly fight them on it stating you believed what you told them to be true. It'd be a tough battle, but, you might have a chance. Depends on the circumstances. If you have 100pts on your license and a history of accidents then it's going to be pretty clear you know you didn't have a clean record, but 1 ticket a few years ago you could honestly forget about exactly when it was.
Lying can also be a problem on other things like:
How many miles do you drive in a year? If you say 5-15K and you really are driving 60K/yr then that would be a problem. It might be hard to tell on a 10yr old car how many miles / yr you are really driving but, on a new car it's not that tough.
If you have done modifications to your car (engine replacement / turbo / nitrous) and didn't tell them that, and get into an accident they could choose not to cover you for all or part of the costs.
Where you live: If you are claiming residence in a place where you don't live to get better rates (perhaps a student living fulltime on campus claiming they live at home on parents policy).
So, as said above, it's best to be very honest w/ them because you don't want to find out a few years later that they won't cover you when you need it. It's really not worth it.