The patent for the four bar linkage (perhaps better known as the Horst
Link) as a bicycle suspension platform is only applicable in the US
and not Canada, Europe, or other countries.
This is true, but the Horst Link patent is not far from its expiration. According to Wikipedia:
"For applications that were pending on and for patents that were still
in force on June 8, 1995, the patent term is either 17 years from the
issue date or 20 years from the filing date of the earliest U.S. or
international (PCT) application to which priority is claimed
(excluding provisional applications), the longer term applying."
The Horst link patent was filed on September 9th, 1994 and issued on April 23rd, 1996. So best case for Specialized, the patent will expire September 9th, 2014.
However, the patent that was granted was a continuation of a patent filed January 21, 1993, and that abandoned patent was a "continuation-in-part" of a patent filed one year earlier to the day. If either of those earlier patents are considered the earliest filing date then The longer of the two terms outlined above would be 17 years after the date of April 23, 1996. That means that the patent would expire the 23rd of next month (April 23rd, 2013). I'm not a patent lawyer, but I would imagine that if Specialized has any grounds to argue that the earlier filings are irrelevant and that the 1994 filing date is the earliest that should be considered, they will do so in court.
How does this affect the design of bikes ridden in the US compared to
countries where it is not patented?
Is the Horst link more popular elsewhere, or does the patent not
restrict the availability of bikes equipped with Horst Link?
Many designs that closely resemble the Horst Linkage but are different enough to avoid patent infringement exist. The classic example is the "faux bar" linkage (as opposed to Horst four bar linkage). The faux bar linkage moves the pivot on the rear of the bike off of the chainstay and onto the seatstay. Among others, Kona and Scott use this design and argue that it works as well if not better than the classic four bar linkage. Some companies license the FSR (Horst link) design from Specialized as well, perhaps the most well known of which is Titus.
My understanding is that designs that would infringe on the Horst Link patent exist in abundance overseas. For instance, that is why Scott entered the US market with hardtails but did not bring their full suspension bikes over until recent years when they switched to a faux bar design.
Am I allowed to import a bike with Horst link suspension into the US,
or would I be breaching the patent?
If a manufacturer/company overseas was selling patent protected goods to US consumers they could be held liable and the goods could be confiscated by customs. For transactions between individuals you would be unlikely to encounter any issues.
As I said, I'm no patent attorney, so take this answer with a grain of salt. I would love to get some eyes from patents.stackexchange.com on this question and answer to ensure that everything I've said here is correct.