Teak wood

You need to check out this site for info on toxic woods. I have turned teak and use lots of dust collection. Short answer, Don't.
http://www.wood-database.com/wood-articles/wood-allergies-and-toxicity/

What's wrong with briar?

Oh, I see.
Pearwood pipes are somewhat common. I've owned one and thought it imparted an odd taste and it didn't hold up as well as briar. But it's cheap and some guys enjoy them.
Rosewood pipes are very cheap substitutes and they're usually what you find in souvenir shops. In my opinion, they're not "real" pipes.
You get what you pay for.

The best wooden pipes are made from briar, or sometimes strawberry wood or morta wood (extremely old wood salvaged from peat bogs). Fruitwoods like cherry and pear are sometimes used in cheaper pipes, and I see a lot of cheap imports using fruit woods stained to look like briar. They'll probably smoke okay, but they won't last as long as a good briar. I've heard of good pipes being made of less commonly available woods like persimmon and osage orange, but those are not widely available.
Many woods other than briar will impart an unpleasant taste to the tobacco smoke. Still, some people like how different woods affect the taste. I know some people who like how black walnut pipes taste; I know others who hate it. But it's important to know ahead of time that the kind of wood can affect the whole experience.
As to toxicity, all wood smoke is considered toxic. I'm not aware of any substantive studies that have been conducted on smoke produced by different kinds of wood, so we're all shooting in the dark about that one. But let's be honest: unless you burn the wall of the tobacco chamber clear through in one smoke, then the vast majority of the smoke entering your mouth from a pipe is coming from the tobacco itself, and I think we're all aware of what that will normally contain.

Teak would make a nice pipe rack though...

If you want an inexpensive pipe, either get a cob or two or go with something like Dr Grabow. Grabow's usually smoke pretty well for not a lot of coin. Most of us have one or two or ten and a lot of folks who have much "nicer" pipes still smoke their Grabow's. (Most of us did not buy a Caminetto or Dunhill when we first started pipe smoking.) I'd take a Grabow over most briar substitutes any day.