I have found that stainless steel pans are fairly easy to clean as long as I soak them in water for 10 minutes first. The one exception to this rule is eggs. They stick! In fact, I just figured out that scrambled eggs are much easier to clean out of a cast iron pan than a stainless steel pan. It's the heaviest cookware, but it will last forever and benefit your health.
Just use a stable fat to grease your pan each time (like coconut oil, butter, clean lard, etc.). I like the taste of coconut oil with eggs and salt.
I use a mild soap and water to soak and then scrub out my cast iron pan with either a wash cloth or a little scrubby pad. I've read that you shouldn't let water drops sit in your cast iron pan or else it will rust. I haven't experienced that, but it's best to dry the pan right away.
I just read this in wikipedia:
Because ordinary cookware cleaning techniques like scouring or washing in a dishwasher will remove or damage the seasoning on a bare cast iron pan, these pans should not be cleaned like most other cookware. Some cast iron aficionados advocate never cleaning cast iron pans at all, simply wiping them out after use, or washing them with hot water and a stiff brush. Others note that grease left on a pan will eventually become rancid, and advocate washing with mild soap and water, and then re-applying a thin layer of fat or oil. A third approach, advocated by television chef Alton Brown, is to scour with coarse salt and a paper towel or clean rag.