Being a Lone Wolf in EVE

Solution 1:

it is possible;

However, the reason why players opt to be part of PvP or pirate corps is for the social, economical and support aspects.

Social; if your new to pirating, having a corp help you out with builds, strategies and locations of populated tunnels in null and low-sec can really make you enjoy the process more. As well, it won't seem so lonely when playing an mmo.

Economical; Some PvP corps (especially the rich ones) help you out with ships and components, including reimbursement for ships you lose. There is also usually joint PvE operations to fund the expensive pirating hobby.

Support; If you get into trouble, you call upon corp or alliance mates to help you out. There is also a lot of fun in small-gang pirating if you wish to dip into that.

Solution 2:

Definitely.
Get a cheap ship, outfit yourself for whatever form of offense will verb your noun, and then go to it.
You can pirate this way, you can fly into nullsec and try to ninja-pop a juicy target, whatever you like.

All you lose out on is that bit of security for when things don't go your way and you don't have a fleet of allies to get you out of the muck.

But the true power of EVE is that there are few game-imposed limits on your style of play. If you want to do it, then you can.

Solution 3:

Oh yes. Check this: http://www.eve-pirate.com/index.php?url=archives/240-The-Death-of-Heikki-High-Stakes-PVP.html&serendipity%5Bcview%5D=linear

Heikki used to be one of the most successful solo pirates in EVE, an insightful story.

Factional Warfare can also work for people looking for solo PvP. 10000 free war targets just by signing to militia, and there's plenty of opportunities for solo kills.