Typical list of solo offlane heroes:
Bounty Hunter (from 6.84, used as a position 4 support instead).
Centaur Warrunner (out of favour in 6.84 onward)
Tusk (also as position 4)
Doom (since the Scorched Earth buff)
Typical Solo Safelane Heroes:
Queen of Pain (QoP)
Some less common solo offlaners are:
Lone Druid (circa patch 6.81)
Earthshaker (with creep blocking trick)
Strange solo offlaners:
These offlaners generally rely on getting levels but not much else:
Ogre Magi (high hp regen, very tough, high armor)
Comment on Solo Laners as of 6.85:
It seems that suicide laners are often defined by their hp regen. For example, Axe & Nightstalker both have superior HP regen, and make excellent offlaners. Nyx has been used in this role for the same reason. Doom is good because of his Scorched Earth, and Broodmother, for her webs. Riki, given the change to his permanent-invis (with regen) may be something that's seen more often as a solo offlaner, largely because he can soak XP and never show his face, if he wants!