Is it worth buying used LEGO?

Yes, for building: used LEGO bricks work like new ones, and complete used sets cost far less than sealed ones. Two things decide what you get: is it complete, and is it genuine LEGO.

Check before you pay

Tick them off as you go:

Genuine LEGO: the word LEGO is molded on the top of each stud. Bricks from other brands do not carry it.
Complete: the set number (on the box or the instructions) lets you check every part. LEGO's building instructions are free on lego.com.
The minifigures: included, and the right ones for that set.
Sealed box: seals intact, box not crushed; that is what collectors pay for.
Missing pieces: ask the seller to list them in writing.

Red flags

"Bulk lot, may not be complete" at the price of a complete set.
"Compatible with LEGO" or "building blocks": usually another brand.
No photo of the minifigures.

Which ones still make sense

Retired sets you missed in stores: used and complete, often far cheaper than sealed.
Mixed bricks sold by weight: cheap for building.
Large sealed retired sets: collector prices.

Live listings on eBay

A few current listings, United States. Asking prices; read each listing's condition and returns.

Sources: LEGO building instructions, free on lego.com; the LEGO logo molded on each stud.