Now in 2019, using pandas 0.25.0 and Python 3.7.3.
(Note : Edited answer to take plotting in account)
Even though I specified just hour,minutes,and seconds I am still getting date. Why is that?
According to pandas documentation I think it's because in a pandas Timestamp (equivalent of Datetime) object, the arguments year, month and day are mandatory, while hour, minutes and seconds are optional.
Therefore if you convert your object-type object in a Datetime, it must have a year-month-day part - if you don't indicate one, it will be the default 1900-01-01.
Since you also have a Date column in your sample, you can use it to have a datetime column with the right dates that you can use to plot :
import pandas as pd
df['Time'] = df.Date + " " + df.Time
df['Time'] = pd.to_datetime(df['Time'], format='%m/%d/%Y %H:%M:%S')
df.plot('Time', subplots=True)
With this your 'Time' column will display values like : 2016-07-25 01:12:07 and its dtype is datetime64[ns].
That being said, IF you plot day by day and you only want to compare times within a day (and not dates+times), having a default date does not seem bothering as long as it's the same date for all times - the times will be correctly compared on a same day, be it a wrong one.
And in the least likely case you would still want a time-only column, this is the reverse operation :
import pandas as pd
df['Time-only'] = pd.to_datetime(df['Time'], format='%H:%M:%S').dt.time
As explained before, it doesn't have a date (year-month-day) so it cannot be a datetime object, therefore this column will be in Object format.