Yes.
How many?
A lot!
Does Craig ever show or talk about his tattoos?
He shows them once in a while. The "snake tat" we see the most often, of course, since it's the most easily seen, even in long-sleeve shirts. But he's displayed them all at one point or another.
Craig talks about his tattoos often, especially now that he has a daily two-hour SiriusXM show. Per one of his chats in March 2017, Craig mentioned that his left arm has a female/magical energy (Ingram Crest, Celtic Knot with wedding date, Raven/Crow), and his right arm has a male/science energy (Ferguson Crest, his boys' names, the Join or Die snake, a compass rose, and the "1st Ascent of Man" Montgolfier balloon.)
On Craig's right shoulder/upper arm is what most refer to as a "Ferguson crest." It was the first tattoo that Craig received, about February 3, 2007, so we've seen it fairly often.
This design is the Ferguson family crest/badge, with the phrase "Dulcius ex aspiris" ("Sweeter after difficulty"), which Craig got in honor of his father, Robert Ferguson. (pic from @randykagan)] Another shot of this tattoo is HERE.
On Craig's left shoulder/upper arm is a tattoo which Craig received in honor of his mother, Janet "Netta" Ingram Ferguson, in September 2009.
The design is a Celtic Cross with the Ingram clan motto, "Magnanimus esto." ("Be great of mind.") (Glimpse and pretty good view from @craigyferg and three screencaps from the 6/9/10 show, by @scottishconan: Pic1 - Pic2 - Pic3. Tattoo can also be seen fairly well during the Moulin Rouge rehearsal of his 8/5/11 Paris show.]
On Craig's right forearm is a "Join or Die" snake tattoo, which he has displayed often, and proudly. Craig received this tattoo in September 2009, after becoming a US citizen.
The design is the political cartoon created by Benjamin Franklin, first published in the Pennsylvania Gazette on May 9, 1754. It depicts a severed snake, with each piece representing a British American colony or region. In 1754, this symbol represented the importance of colonial unity. This tattoo was received about Sept 21, 2009. [First appeared on The View 9/22/2009, and on TLLS 9/28/09; first *displayed* on TLLS 9/29/2009.] Craig told the ladies of The View that he wanted to have an American tattoo, something that was for himself, that was life-affirming, and to him, this tattoo represents new thought and the new world. (pic from @craigyferg. Also a nice shot of it in this musical opening to the 4/5/10 Late Late Show.)]
Craig had often spoken of getting his children's names tattooed on his upper arm, and in Feb 2013, while taping his Super Bowl Special in New Orleans, he asked the audience where a good tattoo place in town was, and they directed him to Electric Ladyland Tattoo, where he got TWO new tattoos - one on each upper arm:
The tattoo on his right arm is of his childrens' names. I won't post a close-up of that one, but you can extrapolate from Craig's self-posted photo above, that it is each child's name on a scroll/ribbon design, one above the other. On his left arm is a Celtic Knot, with the date of his marriage in the center. (As one website describes this design: "the interlacing lines of the Celtic Knot stands for 'no beginning, no ending, the continuity of everlasting love and binding together or intertwining of two souls or spirits.'" Beautiful.)
On March 9, 2017, Craig had a "Tattoo Thursday" event after his SiriusXM show, where he got a raven or crow (he's called it both), on his left arm. Which looks pretty cool when his arm is bent.
On "Tattoo Thursday" April 20, 2017, Craig got another tattoo, a compass rose, because he's "always going to need direction."
In late May 2017 another tattoo made an appearance on Craig's right arm. He's not spoken about this one as of this posting, but it appears to be a depiction of the first ascent of Montgolfier's hot air balloon, but perhaps with the addition of a viking longboat? Take a look: