Is the vein behind your testicles that lead out of them big enough that you should be able to feel. When i check myself i keep feeling it and i wanted to make sure that it is a vein, and not something else, and it is normal for someone to be able to feel it between their fingers.

Yes, you should be able to feel these structures. There are several things you might be feeling around your testicles including the epididymis, vas deferens, veins (and ligaments??). The first two transfer your sperm from the testicles to the prostate area.

Here is a link with some anatomy drawings.
http://www.afraidtoask.com/members/index.html

You can feel several structures such as epididymis, vas deferens, and veins.

When the veins are dilated and increase tortuousity it is known as a varicoele (and has a bag of worms appearance which gets worse when standing up). This is more commonly on the left side. If this is the case you should have your GP check it out as it can result in infertility as the increased blood flow in the veins increases the temperature in the local region to make it hostile to sperm production. Also rare causes for varicoeles need to be excluded such as left renal (kidney) masses which occlude the left testicular vein which drains to the renal system.

Kind Regards
R.