Depends on where you live and what road/vegetation conditions you have to ride through. In some desert areas, I've seen people go all out with armadillo/marathon plus tires with Mr Tuffy's/liners and thorn resistant tubes with slime/sealer. That's a lot of extra weight.
Wal*Mart sells 2 types of slime brand/filled tubes. One of them is the thicker HD/thorn resistant tube and may only come in MTN bike tire sizes...so you have to read the label to get the tube thickness you want and beware of people switching out tubes. They also carry the Bell brand tubes with sealant and some feel the sealant in those tubes is better/thicker.
If you have a road bike and want to use/add your favorite sealant, buy tubes that have a removable presta core. Some feel slime is too thin to be effective in high pressure tubes.
In the end, you have to decide whether or not the weight penalty is worth it or not and how far/much 'flat prevention' is needed.