By "crappiest" I mean a game that's just low quality. Something that is critically panned, turds that are fodder for AVGN reviews.

I have my fair share of shit in my collection. Some of these games I got BECAUSE they are such epic turds.

Some of my smelliest games in no particular order:

Friday the 13th (NES)
Plumbers Don't Wear Ties (3DO) 75 bucks in 2011, but I went into this KNOWING it was donkey shit, and got it to collect.
Shaq Fu (Genesis)
Spawn the Eternal (PS1)
Powerpuff Girls: Chemical X-Traction (N64)
Sonic the Hedgehog 2006 (Xbox 360)... this one was 60 bucks new... OUCH!
Tomcat Alley (Sega CD)
Pac-Man (Atari 2600)
Super Pitfall (NES)
Bill and Ted's Excellent Video Game Adventure (NES)
...and many more. And yes, I do have ET for Atari 2600, but it misses the "shit" category. It falls in the "mediocre" category.

I'd say my biggest turd is Plumbers Don't Wear Ties. It's the only game I have that's on the highest level of AVGN's "Shit Scale", a 6-level scale that AVGN introduced in his Darkwing Duck (TG16) episode. (For the record, I don't have Darkwing Duck for TG-16). In a nutshell, the "Shit Scale" goes like this, and remember that this is AVGN's descriptions:

Level 1: "Debateably bad. Somewhat good games, with serious flaws." Simon's Quest (NES) was in this level.
Level 2: "High level of shit. Possible to play, but no one in their right mind would." He put Dick Tracy, Super Pitfall, and Top Gun (all NES) on this level. These games are pretty bad.
Level 3: "Very high category." He put most LJN games on this level, as well as the CD-i Zelda games.
Level 4: "The severe zone." He put Action 52, Dark Castle (Genesis/CD-i) and the Tiger handheld games here.
Level 5 was just for Dr Jekyll and Mr Hyde, and AVGN fervently hates this one, as he references it in many episodes.
Level 6: "MAJOR CODE RED." This is the level that Big Rigs: Over the Road Racing was on. Plumbers Don't Wear Ties was on this level with it.