This was probably the biggest surprise of all because I don't think it's widely used, particularly here in the US. However, I really, really like it! It doesn't dry too fast while you're rolling it out like other water-based inks do, but it dries to the touch on paper quite fast. It also doesn't require any modifiers and works fine straight out of the tube. I used this ink on my anglerfish print, which I recently finished.
On the downside, it is sort of expensive and you need to roll the ink on your block carefully to avoid leaving lap marks. It isn't widely available (in the US) but you can order it through Dick Blick. If cost isn't a factor for you, it's the logical ink to replace the inferior Speedball and Blick Block Printing Inks.
Honorable Mention - Akua Intaglio
When applied in very thin layers, this ink works alright with linoleum. They also sell an extensive array of ink modifiers (transparent base, mag mix, etc.) to work with. I could see using this on a case-by-case basis, but it wouldn't be me goto linocut ink.
Honorable Mention - Graphic Chemical Water-Soluble Relief Ink
I'm pleased with the printing results of this ink. However, I found the water-soluble vehicle very sticky and messy to work with. Other downsides are that it's not distributed by major retailers here in the US and I wish they'd provide lightfastness ratings for their range of inks.
Least Favorite - Lukas Linol Ink
I'm sorry, but it worked terribly for me and I tried several different colors. Thankfully, it's very hard to buy for those of us in the US.
If you've gotten this far and want to learn more about the linocut process, I've got the lino printing method broken down step-by-step. Now, onto printing on fabric.