I grew up (in the SF reading sense) reading Anderson avidly and, although it's some 15 years since I last read any of his work, remember his writing very fondly and would include several of the 40-odd books I've read among my all time favourites.
I remember an interview with him which was available online (again, probably 15 years ago) in which he listed the books he'd most like to be remembered for. I think said list included
Harvest of Stars, a book I've never read, but otherwise pretty much mirrored my own favourites.
For what it's worth, I'd recommend:
Brainwave (1954) A true classic of its time -- the Earth emerges from a cloud of cosmic dust it has been passing through for centuries and the level of intelligence of all life on the planet takes an abrupt leap forward.
Satan's World (1969) David Falkayne and his crew (one dragon-like alien, one cat-like alien and a wise-cracking ship's computer) bring their own brand of interplanetary trade to an inhospitable world.
Tau Zero (1970) One of the all-time classic hard SF novels. The captain of a starhip full of colonists loses control of his vessel, which keeps accelerating and accelerating and, courtesy of the effects of relativity, carries all in board into a future none of them ever expected to see.
A Midsummer Tempest (1974) A delicious madcap adventure which populates the world with characters from Shakespeare (specifically
A Midsummer Night's Dream and
The Tempest) and throws in all sorts of added spice, including a steam train and even a visit
to The Phoenix -- Andersons own recurring contribution to the genre's list of legendary bars and inns.
As I say, just my own favourites; there are plenty of other great works by him, and I should probably give honourable mention to
The Makeshift Rocket (1962) -- how can a rocketship powered by beer be made to sound so plausible?
Shield (1963) in which a man returns to Earth with a powerful alien object and is pursued by various agencies desperate to claim it and
The High Crusade (1960) which sees a bunch of knights charge a strange 'dragon' and inadvertantly seize control of an alien space ship, which they somehow manage to get into space, where they then set about establishing an empire...
Then there are the
Time Patrol books (so well researched) and the
Ythri... Fine works, all of them.