"Classics are novels of literary significance that have withstood the test of time and remained popular years after their publication." -http://www.wisegeek.org/what-are-classic-novels.htm
"The Swiss Family Robinson" is a classic because it was first published in 1812 and it still remains popular and many people read it today.
This book is relevant to the 21 century because people can still be shipwrecked on uninhabited islands and by reading this book they would find out a lot about creating tools for survival, shelter and what to do in case they encounter wild animals.
The novel might be irrelevant to the 21 century because we have more technology today and so if someone was to be shipwrecked on an island they would probably quickly get rescued and possibly if they had advanced tools with them already would survive on the island very easily.
Yes, I would recommend this book to anyone who likes reading about adventure and survival, with lots of description.