Sweden has thousands of kilometers of hiking trails. The majority leads through the low, often sparsely populated regions. The landscape certainly isn't all stereotype forests and lakes, but also many places of cultural historical interest, towns, villages and countryside.
Trails are well documented and marked, and often looked after by local communities. There are huts, mostly self-service, where you can warm up by a wood-burning stove, dry your clothes and stay overnight. Hundreds of youth hostels are spread about the country, as are many small campsites popular with hikers. Maps of long distance trails are available locally. Do not expect to meet up with hordes of other hikers, and bring enough food. Walking in these low regions is good from early spring until late autumn.
Swedish mountains are a different story altogether. This is rough country, so count on alpine circumstances, and plan your walk between halfway June and halfway September. Most famous is Kungsleden, a trail up north in Lapland. It has existed for almost one hundred years and leads you up Swedens highest mountaintops. More mountainous areas are to be found further south, along the border with Norway. The STF, Swedish Tourist Club, has mountain huts at regular intervals in all these regions.
If all this isn't challenging enough for you, try roaming freely through the Lapland wilderness, without trails or huts, for instance in Sarek National Park.