Reading raw data into geopandas

You can pass the json directly to the GeoDataFrame constructor:

import geopandas as gpd
import requests
data = requests.get("https://data.cityofnewyork.us/api/geospatial/arq3-7z49?method=export&format=GeoJSON")
gdf = gpd.GeoDataFrame(data.json())
gdf.head()

Outputs:

                                            features               type
0  {'type': 'Feature', 'geometry': {'type': 'Poin...  FeatureCollection
1  {'type': 'Feature', 'geometry': {'type': 'Poin...  FeatureCollection
2  {'type': 'Feature', 'geometry': {'type': 'Poin...  FeatureCollection
3  {'type': 'Feature', 'geometry': {'type': 'Poin...  FeatureCollection
4  {'type': 'Feature', 'geometry': {'type': 'Poin...  FeatureCollection

For supported single-file formats or zipped shapefiles, you can use fiona.BytesCollection and GeoDataFrame.from_features:

import requests
import fiona
import geopandas as gpd

url = 'http://www.geopackage.org/data/gdal_sample.gpkg'
request = requests.get(url)
b = bytes(request.content)
with fiona.BytesCollection(b) as f:
    crs = f.crs
    gdf = gpd.GeoDataFrame.from_features(f, crs=crs)
    print(gdf.head())

and for zipped shapefiles (supported as of fiona 1.7.2)

url = 'https://www2.census.gov/geo/tiger/TIGER2010/STATE/2010/tl_2010_31_state10.zip'
request = requests.get(url)
b = bytes(request.content)
with fiona.BytesCollection(b) as f:
    crs = f.crs
    gdf = gpd.GeoDataFrame.from_features(f, crs=crs)
    print(gdf.head())

You can find out what formats Fiona supports using something like:

import fiona
for name, access in fiona.supported_drivers.items():
    print('{}: {}'.format(name, access))

And a hacky workaround for reading in-memory zipped data in fiona 1.7.1 or earlier:

import requests
import uuid
import fiona
import geopandas as gpd
from osgeo import gdal

request = requests.get('https://github.com/OSGeo/gdal/blob/trunk/autotest/ogr/data/poly.zip?raw=true')
vsiz = '/vsimem/{}.zip'.format(uuid.uuid4().hex) #gdal/ogr requires a .zip extension

gdal.FileFromMemBuffer(vsiz,bytes(request.content))
with fiona.Collection(vsiz, vsi='zip', layer ='poly') as f:
    gdf = gpd.GeoDataFrame.from_features(f, crs=f.crs)
    print(gdf.head())

Since fiona.BytesCollection doesn't seem to work for TopoJSON here an solution that works for all without the need of gdal:

import fiona
import geopandas as gpd
import requests

# parse the topojson file into memory
request = requests.get('https://vega.github.io/vega-datasets/data/us-10m.json')
visz = fiona.ogrext.buffer_to_virtual_file(bytes(request.content))

# read the features from a fiona collection into a GeoDataFrame
with fiona.Collection(visz, driver='TopoJSON') as f:
    gdf = gpd.GeoDataFrame.from_features(f, crs=f.crs)

Yes, it is possible now with Fiona (see https://github.com/Toblerity/Fiona/issues/409). I'm not sure if this feature is exposed yet in Geopandas.