In most home settings, a small file cabinet is enough to contain important documents so there's no need for one of those tall, multi-drawer cabinets. Most (if not all) of the small cabinets on this list should be low enough to fit under a desk but you could also use one as a side table if you're lacking space.

Alpha Pedestal from Heartwork — Made in the USA, measures 20-1/4"Hx15-3/4"Wx22-3/4"D, available in six colors. $265

Bisley File Cabinet from Container Store — Available with two or three drawers, measures 16-1/4" x 15-3/4" x 29" h, available in eleven colors. $299

West 18th File Cabinet from Poppin — Three drawers, powder-coated steel, measures 16" x 20" x 24" H, available in four additional colors. $170

MUJI File Cabinet from MoMA Store — Three lockable drawers, measures 24.5h x 15.5w x 22"d, available only in oyster-gray. $285

TPS File Cabinet from CB2 — Three drawers, 15.5"Wx19.75"Dx27.25"H, available in five colors. $159

CopenhagenTwo-Drawer File Cabinet from Room & Board Made in North Dakota, measures 19w 20d 32h, available in five finishes. $679.99

Sentry II Walnut Filing Cabinet from Crate & Barrel Two locking drawers, measures 19.75"Wx22"Dx26"H, available in two wood finishes. $699

Series 11 File Pedestal from Blu Dot Three drawers, measures 18.5" W x 16.5" D x 27" H, available in two finishes. $699
MORE FILE CABINETS ON APARTMENT THERAPY
• Blueprint File Cabinet Makeover
• 10 White & Wonderful Filing Cabinets
• Working File Cabinets Into Your Decor
• Best of Three: Small Metal Filing Cabinets
• Flat Files and Cabinets
(Images: As credited above.)

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Thanks, timely post for me as I've been looking to replace a rickety old desk side filing cabinet I've had since I was a kid (literally).
I opted for the CB2 one in graphite grey. It looks great and seems nice for the price.