According to Meriadoc Brandybuck (Merry), Hobbits are the ones who invented smoking.
They smoke a "variety probably of Nicotiana" (Nicotiana being the Latin name of the plant family to which tobacco belongs).
The best home-grown pipe-weed comes from Southfarthing, and the best-known varieties are Longbottom Leaf, Old Toby, and Southern Star.
Merry concludes that pipe-weed must have originally come from Gondor in the South, but "Hobbits first put it into pipes. Not even the Wizards first thought of that before we did" (prologue.2.4). That's more information than we ever needed to know about Hobbit pipe-weed.