First, a little background:

When squid mate, a male transfers its sperm to a female enclosed in complex structures called spermatophores. These are accumulated in the spermatophoric sac, a storage organ inside the mantle cavity, before ejaculation through the penis. Squid that spawn in shelf waters and epipelagic waters of the open ocean usually have short penes hidden completely inside the mantle. Males pick the ejaculated spermatophores from inside their mantle with a specially modified arm called the hectocotylus, to transfer them to the female. Females spawning in shallow water have special places for spermatophore attachment on the body, both externally (skin ring around the mouth, and back of the head) and internally (oviducal gland openings near gills) (Nesis, 1995). As female squid lack a vagina, the use of a highly articulated arm (hectocotylus) for transfer and placement of spermatophores is more precise than by means of the comparatively poorly articulated penis.

So male squid have penises deep in their mantle. Many species have short penises, and they also have a specialized arm, the hectocotylus, that they use to reach in to their own mantle to scoop up ejaculate and then place it in the appropriate place in a female.

Other species lack the hectocotylus, but instead have a long penis, as some investicators discovered. They are also capable of erections, which was a surprise.

A mature moribund male of the greater hooked squid Onykia ingens (Smith, 1881) (38.5 cm mantle length, 1180 g body mass) was caught on the Patagonian slope south of the Falkland Islands (July 2006, 53°20′S, 59°31′W, 1050 m depth). When the mantle of the squid was opened for maturity assessment during processing of the catch onboard, the penis of the squid, which previously had extended only slightly beyond the mantle margin, suddenly started to erect. It became rigid and quickly elongated to 67 cm total length, almost the same length as the whole body of the animal (mantle, head and arms; Fig. 1). Immediately after elongation, several spermatophores were ejaculated from the penis tip.

So not only do they have penises capable of erection, they can get erections when dead and partially dissected, which means I can now show you a zombie squid dick pic.

Mature males of deep-water squid Onykia ingens with cut-open mantles showing non-erect (A) and fully erect (B) penes.

(blame Tommy Leung)

Arkhipkin AI, Laptikhovsky VV (2010) Observation of penis elongation in Onykia ingens: implications for spermatophore transfer in deep-water squid, Journal of Molluscan Studies 76(3):299–300.