Pi Day, Pi Minute, or Pi Second?

Javascript (ES6), 114 112 - 15 = 97 bytes

x=>['Pi Day','Pi Minute','Pi Second'].find((x,i)=>[/ar 14/,/(03|15):14:/,/03:14/][i].test(Date()))||'No Pi Time'

Ungolfed:

x=>
['Pi Day', 'Pi Minute', 'Pi Second']  // array of outputs
.find(                                // find first element in the array
    (x, i)=>                          // which returns truthy for this function
    [/ar 14/, /(03|15):14:/, /03:14/] // array of regex patterns
    [i]                               // get corresponding regex based on index
    .test(Date())                     // test it against current date, date is automatically cast to string
) || 'No Pi Time'                     // if no result, then return "No Pi Time"

Thanks for -2 bytes @edc65

Ruby, 125 124 chars

i=[*[(t=Time.new).month,t.day,t.hour,t.min,t.sec].each_cons(2)].index [3,14];i&&$><<['Pi Day','','Pi Minute','Pi Second'][i]

Alas, the cleverer %i[month day hour min sec].map{|x|Time.new.send x} is longer.

The key here is the use of each_cons to avoid repetition (see the last few lines of the explanation below).

i=                          # send i (index) to...
[*                          # convert to array (splat)...
 [
  (t=Time.new).month,       # the current month...
  t.day,t.hour,t.min,t.sec  # etc... (duh)
 ]
 .each_cons(2)              # each consecutive two elements
]                           # [[month, day], [day, hour], [hour, min], etc]
.index [3,14];              # first occurrence of [3, 14]
i&&                         # shorthand for "if i"...
$><<                        # output...
[
 'Pi Day',                  # [month=3, day=14] is Pi Day
 '',                        # [day=3, hour=14] isn't anything
 'Pi Minute',               # [hour=3, min=14] is Pi Minute
 'Pi Second'                # [min=3, sec=14] is Pi Second
][i]                        # index by index (obviously)

Python 2, 219 186 183 Bytes (198-15)

_{I tried}

Ungolfed:

from datetime import datetime

now = datetime.now()
output = ['Pi Day', 'Pi Minute', 'Pi Second', 'No Pi Time']

if now.month == 3 and now.day == 14:
    print output[0]
elif now.hour == 2 and now.minute == 13:
    print output[1]
elif now.minute = 2 and now.second == 13:
    print output[2]
else:
    print output[3]

Golfed:

from datetime import *
n=datetime.now()
a=n.minute
if n.month==3and n.day==14:print'Pi Day'
elif n.hour==2and a==13:print'Pi Minute'
elif a==2and n.second==13:print'Pi Second'
else:print'No Pi Time'