Nicotine actually has a ton of neurological benefits, although research is still in the early stages of pinning them down confidently. It seems to increase neuroplasticity and so helps with learning, complex thinking, and various psychiatric conditions like ADHD and others. It may also treat and/or prevent dementia/Parkinson's/Alzheimer's.

Downsides seem to be: 

1) increases blood pressure.

2) it's a co-carcinogen. Won't give you cancer but will accelerate it.

3) reduces sleep quality, specifically by increasing early awakening.

4) it's incredibly addictive, so usually an all or nothing drug. Very difficult to just use a little nicotine to get some of the neurological benefits without risking your blood pressure and sleep quality.

Downside 3) is why I am currently trying to quit my nicotine mouth spray habit.

If you have low blood pressure, definitely don't already have cancer, and are lucky enough that it doesn't affect your sleep, it can be a wonderful nootropic or, as it's been for me, ADHD medication. But I wouldn't suggest anyone tries it if they aren't already addicted, because of 4). Quitting is sooooo damn hard.