Worst keyboard ever? This horrible no-name membrane board I bought at a thrift store when I was building my first system.
Worst mechanical though would be this Adesso full-size Cherry MX Blues keyboard I bought my mom for 65 bucks on Newegg back in 2011. That thing was horrible. Some of the keycaps would stick, the space bar kept catching the chassis, and the keys themselves felt horribly scratchy (although this was probably the complete lack of finishing on the keycaps). My mom accidentally spilled a coke on the thing, and we took that as a sign that a better keyboard was needed.
So I bought myself a Rosewill RK9000BR to replace my original RK9000 (fixed cord model), gave her the old version keyboard, and she was AMAZED at the difference in quality. (To be fair, she'd used it before, which is why I bought a keyboard with Blues). She almost stole the BR when it arrived, but didn't like the feel of the keys. I'd have let her have it, too, if she wanted it.