If I walked into an exposed pipe that sticks out of an apartment building but I was on the legal sidewalk, is the apartment owner liable?

The first issue is whether having pipe sticking out the way it did is negligent, or unreasonably careless. It's not uncommon for pipes, or fire sprinkler attachments, or gutters/downspouts, or  wires (e.g. cable), or antennae (e.g. Direct TV), etc. to protrude from buildings; the fact that something was sticking out is not automatically negligent. However, if the pipe sticking out was sticking out unreasonably far or was something which would not normally stick out, then the landlord or owner may have had an obligation to do something about it to avoid harm. So based on the specific facts, it may nor may not have been negligent; and if not negligent, it is very unlikely there would be any liability.

Second, you can only recover an amount commensurate with your injury, even if there is liabiltiy. If you have not incurred significant medical bills, have not lost significant wages, and/or have not suffered some at least moderately long last disability (e.g. an arm is impaired; you have blurry vision; you're having trouble eating or talking due to injury to your jaw; etc.), it  is difficult to imagine that legal action would be economically worth it.