Comparatively expensive, but the easiest and best I've found - and I've bought and used a bunch of different kinds.
http://www.themoletrap.com/

I saw this a while back - but using it actually seems to heave the ground a bit. Not cheap either, but probably very gratifying ;)

http://www.rodenator.com/

I already know how to convert dog poo into gold...

I had a Jack Russel Terrier, god rest her soul, who was a great moler... she is long gone, but we had a yellow lab pup, before the great moler passed away. The JRT taught the lab how to be a good mole dog. Unfortunately the lab makes a larger hole than the JRT did. The lab is turning out to be a great varmint dog, she caught two moles, one vole, and two chipmunks over the last three weeks.

I think mole control is like weed control. Its never once and done, its a continual process.

I have noticed that when you grow your grass tall, the mole tunnels are less visually obvious, hidden by the tall grass.

I had a horrible mole problem and dropped Talpirid poison worms into cones after they appeared.

I haven't had another mole issue since - and that was the summer of 2006. It's pricey, but it works.

Thanks to all for your replies!
Notes: I'll keep that trap in mind, seems to work on the same principal of the three or four different types I already have in the shed, but it does look easier to set than some.

Joepyeweed: I have already experimented with the method, that the rodenator is based on. It has a lot of problems, even assuming that you don't have to fork out the 2-3 thousand they want for their unit (which of course a slightly re-dressed shop oxy-acetelene torch outfit).
The company provides a link to a study carried out by one of the state agriculture departments(Montana I think)which showed pretty good results when the unit was used on gophers. However the study also noted that activity went back to near the previous levels within a very short time 7-10 days. It was speculated that this was due to in-migration. Because of the large amount of re-application, the high cost of bottled oxygen, and the volatility of the process, this one falls short of the "dog poo prise", but thanks and keep thinkin.

Wcnitz: OK, I have run across references to this before, sounds interesting, where did you aquire these "Talpirid worms" and what was the cost (in 2006 anyway)?

That trap is heavy duty. Setting it with your foot isn't just a convenience. The spring is so strong, you have to set it that way.
Another advantage is that the "claws" get spread apart when they're under the ground. They create and clean out their own trench so when they do close there's no obstruction in the way - except for the mole. ;=)
Let me know if you go with the worm bait. I read a trick about using it. Don't know whether or not it works, but it sounded logical.

Talpirid runs about $35-$45 for twenty worms. See the below link.

Here is a link that might be useful: Talpirid

Your problem is not moles. Moles are simply a symptom of your real problem. Grubs. Use a granular insect and grub killer and follow the directions for proper application. Once you eliminate the source of the moles' food your mole problem should disappear.

I disagree with Tommy. While the do eat grubs, one of moles' favorite foods is earthworms. I have not seen any grubs in my lawn, but I do have a ton of earthworms. The moles love tearing up my yard going after the worms. I suspect that by killing the grubs, you also are killing the earthworms, which will cure your mole problem but cause further problems with your soil.

CAn we visit this mole issue again??? They are driiving me nutty. Has anyone tried Juicy Fruit gum? I treid it today at the advice of an old gentleman. He is probably chuckling now!!

Take it from one who has tried all the gimmics (except the worms) including the poisons and a proud owner of a rodenator. None of them are fool proof. All of them work but not all the time. The rodenator is sure fun to use, makes a mess of your yard with shallow tunnels, and is not a gaurantee. Migration is a definite problem once you do catch the original invader. This morning I used my 12 gauge, a lawn chair, and some patience to bag one. I have been out every day this week blowing up holes. They just don't stop. Guess I'll invest in some worms next! Good luck