file_count = len([f for f in os.walk(".").next()[2] if f[-4:] == ".txt"])

# to also count mixed case file extensions like .TXT or .Txt etc.
# use module glob ...
import glob
 
# use current directory
# or change with os.chdir(directory_name)
print "Number of .txt files =", len(glob.glob("*.txt"))

import os
path = ('c:\\stuff\\countfiles\\')
print "Counting all .txt files in: " + path
x=0
for files in os.listdir(path):
    if files.endswith('.txt'):
        x+=1
        print "\nFile #" + str(x) + ": " + files
print "\nTotal number of .txt files in: " + path + " -"
print x

import os, sys
print "Total: %d .txt files" % len(map(lambda f: sys.stdout.write(f+"\n"),sorted(filter(lambda f: f.endswith(".txt"), os.listdir(".")))))