Solo (Off)Laners

A solo offlaner is typically a hero with some escape ability, healing, or is very tough, so they can get close enough to get XP even against a tri-lane.  Others have the ability to slow or delay the creeps (such as Enigma, Earthshaker or Lich), to enable them to gain XP as their tower kills the creeps.

Typical list of solo offlane heroes:
Bounty Hunter (from 6.84, used as a position 4 support instead).
Timbersaw
Centaur Warrunner (out of favour in 6.84 onward)
Beastmaster
Clockwerk
Dark Seer
Axe
Undying
Spiritbreaker
Tusk (also as position 4)
Phoenix
Broodmother
Doom (since the Scorched Earth buff)

Typical Solo Safelane Heroes:
Nature's Prophet
Weaver
Lone Druid
Doom
Razor
Puck
Queen of Pain (QoP)

Some less common solo offlaners are:
Puck
Magnus
Phoenix
Broodmother
Clinkz
Slark
Windranger
Batrider
Bristleback
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:

Sand King

Lich

Tidehunter

Treant
Jakiro
Mirana
Enigma
Venomancer
Ogre Magi (high hp regen, very tough, high armor)
Omniknight

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!