If you can afford it, the Okko Basstard is really nice. The "+" control is a nice feature for me, because I like grit but having lots of drive just isn't so nice for some tunes. Very warm overdrive, reminds me of a cranked tube pre-amp. It also seems to play very nicely with other preamps, like the Bass Driver I feed it into.
Before that, I used a DOD FX-91 I modded with 1N4002 clipping diodes and a JRC4558 opamp as well as a single resistor mod (Spoiler: it's a modified Tube Screamer) and liked the tone of that as well, especially cranked. The blend control on that is a little meh, but it works.
If you don't mind some noise, the Ibanez PD-7 is a nice overdrive I used for a while as well. The attack switch was an interesting touch. I had one that I overhauled all the cheap mylar caps with polypropylene film, and that took care of almost all the hiss. If only Ibanez had re-made it with a footswitch between OD and Distortion.
Marshall Guv'nor is an okay one as well, a lot of guys have good luck with it but I always felt like the tonestack was a major weak point of that that killed it for me. The ProCo Rat can work as well, but those seem to suck out lows even with big input caps and coupling caps. I think the filtering has something to do with it.
A Fulltone Bass-Drive MOSFET is a nice one too, if you can find one and drop that kind of coin. It always reminds me of the driven tone on Soundgarden's Spoonman. I was kind of stuck between that and the OKKO for a while, but I found the Basstard at a lower price than the Fulltone.
These are ones I've had experience with and thought were good...but some are considered boutique.