Five. (You have to have an odd number... he was told that by a tattoo artist.)
Does Craig ever show his tattoos?
Yes, some more than others. The "snake tat" we see the most often, but the tattoos on his left and right shoulder/upper arm, due to their location, aren't as easy to "show off" as the one on his forearm, so you'll see those less often. Usually only during skits that involve him being sleeveless. Is probably just luck that we happen to see one more often than the other.
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 has often spoken of getting his children's names tattooed on his upper arm. No word that he's actually done so. However... *update 2/5/2013*:
While in New Orleans, taping his Super Bowl Special, Craig asked the audience where a good tattoo place in town was, and they directed him to Electric Ladyland Tattoo, where he got what appears to be TWO new tattoos - one on each upper arm:
Craig also tweeted about this event:
Craig confirmed, during a 2/5/13 interview with Adhir Kalyan, that he did, in fact, get two more tattoos, bringing the total number to five. He has not yet revealed what designs he got, but I'm sure he'll tell us more as time goes on.
You can catch a glimpse of both of Craig's new tattoos in a photo he tweeted on March 23, 2013:
And a slightly closer -- yet still a bit fuzzy -- view of the one on his right arm:
Update: During a Feb 7, 2014 interview with Sarah Paulson, Craig noted that he got his kids' names tattooed on his right arm and "something else" on the left.