Maybe there is a better way, but how about:

import glob
types = ('*.pdf', '*.cpp') # the tuple of file types
files_grabbed = []
for files in types:
    files_grabbed.extend(glob.glob(files))

# files_grabbed is the list of pdf and cpp files

Perhaps there is another way, so wait in case someone else comes up with a better answer.

There are a couple of ways:

pathlib.Path().rglob()

Use pathlib.Path().rglob() from the pathlib module, which was introduced in Python 3.5.

from pathlib import Path

for path in Path('src').rglob('*.c'):
    print(path.name)

glob.glob()

If you don't want to use pathlib, use glob.glob():

from glob import glob

for filename in glob('src/**/*.c', recursive=True):
    print(filename)   

For cases where matching files beginning with a dot (.); like files in the current directory or hidden files on Unix based system, use the os.walk() solution below.

os.walk()

For older Python versions, use os.walk() to recursively walk a directory and fnmatch.filter() to match against a simple expression:

import fnmatch
import os

matches = []
for root, dirnames, filenames in os.walk('src'):
    for filename in fnmatch.filter(filenames, '*.c'):
        matches.append(os.path.join(root, filename))

This version should also be faster depending on how many files you have, as the pathlib module has a bit of overhead over os.walk().

For python 2.7: pip install glob2

For python 3.7: pip3 install glob2

The glob module uses the fnmatch module for individual path elements.

That means the path is split into the directory name and the filename, and if the directory name contains meta characters (contains any of the characters [, * or ?) then these are expanded recursively.

If you have a list of strings that are simple filenames, then just using the fnmatch.filter() function is enough:

import fnmatch

matching = fnmatch.filter(filenames, pattern)

but if they contain full paths, you need to do more work as the regular expression generated doesn't take path segments into account (wildcards don't exclude the separators nor are they adjusted for cross-platform path matching).

You can construct a simple trie from the paths, then match your pattern against that:

import fnmatch
import glob
import os.path
from itertools import product


# Cross-Python dictionary views on the keys 
if hasattr(dict, 'viewkeys'):
    # Python 2
    def _viewkeys(d):
        return d.viewkeys()
else:
    # Python 3
    def _viewkeys(d):
        return d.keys()


def _in_trie(trie, path):
    """Determine if path is completely in trie"""
    current = trie
    for elem in path:
        try:
            current = current[elem]
        except KeyError:
            return False
    return None in current


def find_matching_paths(paths, pattern):
    """Produce a list of paths that match the pattern.

    * paths is a list of strings representing filesystem paths
    * pattern is a glob pattern as supported by the fnmatch module

    """
    if os.altsep:  # normalise
        pattern = pattern.replace(os.altsep, os.sep)
    pattern = pattern.split(os.sep)

    # build a trie out of path elements; efficiently search on prefixes
    path_trie = {}
    for path in paths:
        if os.altsep:  # normalise
            path = path.replace(os.altsep, os.sep)
        _, path = os.path.splitdrive(path)
        elems = path.split(os.sep)
        current = path_trie
        for elem in elems:
            current = current.setdefault(elem, {})
        current.setdefault(None, None)  # sentinel

    matching = []

    current_level = [path_trie]
    for subpattern in pattern:
        if not glob.has_magic(subpattern):
            # plain element, element must be in the trie or there are
            # 0 matches
            if not any(subpattern in d for d in current_level):
                return []
            matching.append([subpattern])
            current_level = [d[subpattern] for d in current_level if subpattern in d]
        else:
            # match all next levels in the trie that match the pattern
            matched_names = fnmatch.filter({k for d in current_level for k in d}, subpattern)
            if not matched_names:
                # nothing found
                return []
            matching.append(matched_names)
            current_level = [d[n] for d in current_level for n in _viewkeys(d) & set(matched_names)]

    return [os.sep.join(p) for p in product(*matching)
            if _in_trie(path_trie, p)]

This mouthful can quickly find matches using globs anywhere along the path:

>>> paths = ['/foo/bar/baz', '/spam/eggs/baz', '/foo/bar/bar']
>>> find_matching_paths(paths, '/foo/bar/*')
['/foo/bar/baz', '/foo/bar/bar']
>>> find_matching_paths(paths, '/*/bar/b*')
['/foo/bar/baz', '/foo/bar/bar']
>>> find_matching_paths(paths, '/*/[be]*/b*')
['/foo/bar/baz', '/foo/bar/bar', '/spam/eggs/baz']

The scope of the for loop defines what is done for each file. Everything after the for loop is only done once:

 import os                                                                   
 import glob                                                                 
 os.chdir('C:\Users\U2970\Documents\Arcgis\Text_files\Data_exports')         
 for file in list(glob.glob('*.txt')):                                       
     reader = open(file)               # <-- Things done for each file

 # Things done only once:                      
 from EXPORT_COLUMN_SET import *                                             

 try:                                                                        
      data = column_set(reader)                                              
      data.start_data_printer()                                              
 finally:                                                                    
      reader.close()   

You can indent the rest of the code to put it inside the for loop:

 import os                                                                   
 import glob                                                                 
 os.chdir('C:\Users\U2970\Documents\Arcgis\Text_files\Data_exports')       
 for file in list(glob.glob('*.txt')):                           
     reader = open(file)                  # ^                 
                                          # |                
     from EXPORT_COLUMN_SET import *      # |              
                                          # | Things now done for each file
     try:                                 # |                                 
          data = column_set(reader)       # |                              
          data.start_data_printer()       # |                              
     finally:                             # |                              
          reader.close()                  # v