Here's a regex solution since top voted regex doesn't work for weird cases like top-level domain. Some test cases down below.
regex = re.compile(
    r"(\w+://)?"                # protocol                      (optional)
    r"(\w+\.)?"                 # host                          (optional)
    r"(([\w-]+)\.(\w+))"        # domain
    r"(\.\w+)*"                 # top-level domain              (optional, can have > 1)
    r"([\w\-\._\~/]*)*(?<!\.)"  # path, params, anchors, etc.   (optional)
)
cases = [
    "http://www.google.com",
    "https://www.google.com",
    "http://google.com",
    "https://google.com",
    "www.google.com",
    "google.com",
    "http://www.google.com/~as_db3.2123/134-1a",
    "https://www.google.com/~as_db3.2123/134-1a",
    "http://google.com/~as_db3.2123/134-1a",
    "https://google.com/~as_db3.2123/134-1a",
    "www.google.com/~as_db3.2123/134-1a",
    "google.com/~as_db3.2123/134-1a",
    # .co.uk top level
    "http://www.google.co.uk",
    "https://www.google.co.uk",
    "http://google.co.uk",
    "https://google.co.uk",
    "www.google.co.uk",
    "google.co.uk",
    "http://www.google.co.uk/~as_db3.2123/134-1a",
    "https://www.google.co.uk/~as_db3.2123/134-1a",
    "http://google.co.uk/~as_db3.2123/134-1a",
    "https://google.co.uk/~as_db3.2123/134-1a",
    "www.google.co.uk/~as_db3.2123/134-1a",
    "google.co.uk/~as_db3.2123/134-1a",
    "https://...",
    "https://..",
    "https://.",
    "https://.google.com",
    "https://..google.com",
    "https://...google.com",
    "https://.google..com",
    "https://.google...com"
    "https://...google..com",
    "https://...google...com",
    ".google.com",
    ".google.co."
    "https://google.co."
]
for c in cases:
    print(c, regex.match(c).span()[1] - regex.match(c).span()[0] == len(c))
Edit: Added hyphen to domain as suggested by nickh.