Ok...I just had to put my two cents worth on one of favorite things on the planet.
If you're just starting to drink Scotch, start with a lighter malt like Dalwhinnie or Glenlivet 18. Glenlivet 18 was the first Scotch I tried that I really liked.
Highland malts are usually the most approachable for a first time drinker. They tend to be a little lighter in style, although they're are exceptions. Speyside is in this region and accounts for the majority of distilleries in Scotland.
The Lowlands malts tend to lean toward a more grassy herbacious style. Some ditilleries were mentioned before, but my favorite from the area is Littlemill.
Isaly malts are my favorite. Lagavulin is probably the most famous. However, if you can find a bottle of Port Ellen, then grab it. The distillery closed in 1983, so you'll have to look for an Independent Bottling from a company such as Cadenhead's.
Finally, there is Campbeltown. Only two distilleries exist there now, Springbank and Glen Scotia. These are very interesting malts in that they exhibit a little of all the regions in there flavors. Check them out.
My personal all-time list..
1983 Cragganmore
Ledaig 20 year old (from the Isle of Mull)
Glenturret 18 year old
1977 Glenlochy
Inchmurrin 20 year old
Port Ellen 17 year old Cask Strength
Littlemill 8 year old
1979 Lagavulin Doubled Matured
(This version of Lagavulin was finished in Pedro Ximenez Sherry casks.
~)