Collecting out of circulation got a shot in the arm when the Statehood Quarters were introduced in 1999. Putting a set together led to some new collectors discovering the long Washington quarter series. But there is another long series--over 70 years now--that can be fun to collect.
Roosevelt dimes were first minted in 1946, one year after the death of FDR. They are still being minted, with no changes in type or design. Most from 1965, if not all, can be found in circulation. Perhaps a family member has an accumulation of silver coins that may contain some of the silver issues.
Finding nice clads can be a challenge. Some of the dates do not show up with great frequency, so there is the thrill of the chase. The 1969 and 1973 coins come to mind. There is one collector-only issue, the 1996-W, minted at West Point.
Varieties can spice up this set, such as the 1982 no mintmark. I've heard of many of these showing up in change.
Beginning collectors, or older collectors who want to relive collecting from change, may do well to look at Roosevelt dimes.