diff --git a/dvc/config.py b/dvc/config.py
--- a/dvc/config.py
+++ b/dvc/config.py
@@ -198,6 +198,7 @@ class Config(object):  # pylint: disable=too-many-instance-attributes
     SECTION_REMOTE_ASK_PASSWORD = "ask_password"
     SECTION_REMOTE_GSS_AUTH = "gss_auth"
     SECTION_REMOTE_NO_TRAVERSE = "no_traverse"
+    SECTION_REMOTE_VERIFY = "verify"
     SECTION_REMOTE_SCHEMA = {
         Required(SECTION_REMOTE_URL): str,
         SECTION_AWS_REGION: str,
@@ -232,6 +233,7 @@ class Config(object):  # pylint: disable=too-many-instance-attributes
         SECTION_GDRIVE_USER_CREDENTIALS_FILE: str,
         PRIVATE_CWD: str,
         SECTION_REMOTE_NO_TRAVERSE: Bool,
+        SECTION_REMOTE_VERIFY: Bool,
     }
 
     SECTION_STATE = "state"
diff --git a/dvc/data_cloud.py b/dvc/data_cloud.py
--- a/dvc/data_cloud.py
+++ b/dvc/data_cloud.py
@@ -73,13 +73,25 @@ def pull(self, cache, jobs=None, remote=None, show_checksums=False):
             show_checksums (bool): show checksums instead of file names in
                 information messages.
         """
-        return self.repo.cache.local.pull(
-            cache,
-            jobs=jobs,
-            remote=self.get_remote(remote, "pull"),
-            show_checksums=show_checksums,
+        remote = self.get_remote(remote, "pull")
+        downloaded_items_num = self.repo.cache.local.pull(
+            cache, jobs=jobs, remote=remote, show_checksums=show_checksums
         )
 
+        if not remote.verify:
+            self._save_pulled_checksums(cache)
+
+        return downloaded_items_num
+
+    def _save_pulled_checksums(self, cache):
+        for checksum in cache["local"].keys():
+            cache_file = self.repo.cache.local.checksum_to_path_info(checksum)
+            if self.repo.cache.local.exists(cache_file):
+                # We can safely save here, as existing corrupted files will be
+                # removed upon status, while files corrupted during download
+                # will not be moved from tmp_file (see `RemoteBASE.download()`)
+                self.repo.state.save(cache_file, checksum)
+
     def status(self, cache, jobs=None, remote=None, show_checksums=False):
         """Check status of data items in a cloud-agnostic way.
 
diff --git a/dvc/remote/base.py b/dvc/remote/base.py
--- a/dvc/remote/base.py
+++ b/dvc/remote/base.py
@@ -80,6 +80,7 @@ class RemoteBASE(object):
     CHECKSUM_JOBS = max(1, min(4, cpu_count() // 2))
     DEFAULT_CACHE_TYPES = ["copy"]
     DEFAULT_NO_TRAVERSE = True
+    DEFAULT_VERIFY = False
 
     state = StateNoop()
 
@@ -93,6 +94,9 @@ def __init__(self, repo, config):
         self.no_traverse = config.get(
             Config.SECTION_REMOTE_NO_TRAVERSE, self.DEFAULT_NO_TRAVERSE
         )
+        self.verify = config.get(
+            Config.SECTION_REMOTE_VERIFY, self.DEFAULT_VERIFY
+        )
         self._dir_info = {}
 
         types = config.get(Config.SECTION_CACHE_TYPE, None)
diff --git a/dvc/remote/gdrive.py b/dvc/remote/gdrive.py
--- a/dvc/remote/gdrive.py
+++ b/dvc/remote/gdrive.py
@@ -63,6 +63,7 @@ class RemoteGDrive(RemoteBASE):
     path_cls = CloudURLInfo
     REQUIRES = {"pydrive2": "pydrive2"}
     DEFAULT_NO_TRAVERSE = False
+    DEFAULT_VERIFY = True
 
     GDRIVE_USER_CREDENTIALS_DATA = "GDRIVE_USER_CREDENTIALS_DATA"
     DEFAULT_USER_CREDENTIALS_FILE = "gdrive-user-credentials.json"

Hi @BernMcCarty !

Sorry for the delay. This is a great request! It was designed to be a bit paranoid about checksums, but thinking about it right now, dvc has been verifying checksums before pushing for a long time now. Plus, all of the remotes are pretty reliable and do consistency checks while uploading/downloading chunks of data. Overall, it seems pretty reasonable to me to adopt that as a default behaviour.

To accomplish that, we could make `RemoteLOCAL.pull`(or somewhere around that) push md5 entries into our state db(see `self.state.save(path_info, checksum)`) after it has successfully downloaded a cache file.
diff --git a/tests/func/test_data_cloud.py b/tests/func/test_data_cloud.py
--- a/tests/func/test_data_cloud.py
+++ b/tests/func/test_data_cloud.py
@@ -9,10 +9,11 @@
 from mock import patch
 
 from dvc.cache import NamedCache
+from dvc.compat import fspath
 from dvc.config import Config
 from dvc.data_cloud import DataCloud
 from dvc.main import main
-from dvc.remote import RemoteAZURE
+from dvc.remote import RemoteAZURE, RemoteConfig
 from dvc.remote import RemoteGDrive
 from dvc.remote import RemoteGS
 from dvc.remote import RemoteHDFS
@@ -653,3 +654,37 @@ def test(self):
         assert self.message_header in self._caplog.text
         assert self.message_foo_part in self._caplog.text
         assert self.message_bar_part in self._caplog.text
+
+
+def test_verify_checksums(tmp_dir, scm, dvc, mocker, tmp_path_factory):
+    tmp_dir.dvc_gen({"file": "file1 content"}, commit="add file")
+    tmp_dir.dvc_gen({"dir": {"subfile": "file2 content"}}, commit="add dir")
+
+    RemoteConfig(dvc.config).add(
+        "local_remote",
+        fspath(tmp_path_factory.mktemp("local_remote")),
+        default=True,
+    )
+    dvc.push()
+
+    # remove artifacts and cache to trigger fetching
+    os.remove("file")
+    shutil.rmtree("dir")
+    shutil.rmtree(dvc.cache.local.cache_dir)
+
+    checksum_spy = mocker.spy(dvc.cache.local, "get_file_checksum")
+
+    dvc.pull()
+    assert checksum_spy.call_count == 0
+
+    # Removing cache will invalidate existing state entries
+    shutil.rmtree(dvc.cache.local.cache_dir)
+
+    dvc.config.set(
+        Config.SECTION_REMOTE_FMT.format("local_remote"),
+        Config.SECTION_REMOTE_VERIFY,
+        "True",
+    )
+
+    dvc.pull()
+    assert checksum_spy.call_count == 3

option to have dvc pull trust the remote and not calculate its own MD5 hashes
The dvc pull command takes the time (which can be significant it seems) to calculate its own MD5 hashes. It would be nice if there were an option to tell it to trust the remote and skip this so that it would complete faster.  Or it could trust the remote by default and make you opt-in to recalculating the hashes if that is what you really wanted. It seems unlikely that it would be a bad breaking change to flip the default behavior here.  Or, maybe, we just don't need dvc pull to _ever_ calculate MD5 hashes. Thoughts?

tests/func/test_data_cloud.py::test_verify_checksums
tests/func/test_data_cloud.py::TestRemoteLOCAL::test tests/func/test_data_cloud.py::TestRemoteSSHMocked::test tests/func/test_data_cloud.py::TestDataCloudErrorCLI::test_error tests/func/test_data_cloud.py::TestWarnOnOutdatedStage::test tests/func/test_data_cloud.py::TestRecursiveSyncOperations::test tests/func/test_data_cloud.py::TestCheckSumRecalculation::test tests/func/test_data_cloud.py::TestShouldWarnOnNoChecksumInLocalAndRemoteCache::test