question

[Sundance]

Thanks.

[jackelope]

There aren't any OTC goat or sheep tags in the lower 48. You can go to BC and hunt them with a guide.
Pretty much most of the western states have goats and sheep to hunt. Maybe the best odds are in Idaho? They require up-front money. Montana, Wyoming, Nevada, Utah, etc all have goats and sheep. Odds suck everywhere but you gotta be in it to win it. (I am not in it  )
A lot of the states require that you front the cost of the tag if you apply. If you don't draw, you get a refund. Most guys use credit cards for this.

[ramslam]

Actually there is an OTC sheep hunt in the lower 48.  Montana has an area referred to as the "Unlimited" sheep units.  If you apply you are guarenteed to draw.  It is rugged, rugged, rugged and success rate is low, low, low.

[shanevg]

OTC tags are in BC and Alaska w/ a guide and Montana for sheep with low success a la ramslam.

As for applying:
Idaho has some of the best odds but you don't accrue points.  You need to upfront the ~$2300 tag cost just to apply.
MT has decent odds, you do gain points, you need to upfront the ~$800 to apply.
Wyoming has mediocre odds, you are probably too far behind in the points game to ever get drawn for sheep but you either need to upfront tag costs or buy a point for $100.  There are no points for goat in Wyoming so you just up front the $1800 and play your luck, roughly 1 in 100 odds. 
Oregon has good sheep odds for non-residents but you need to buy a non-refundable license to apply.  No points for sheep and no NR applications for goat.
Utah has some terrible odds for sheep and mediocre odds for goat with non-refundable license and points.
Colorado has decent odds for both sheep and goats, need to upfront $1800 tag fee and have at least 3 preference points before eligible for tag. 
Arizona has sheep, upfront non-refundable license and upfront tag cost with bad odds. 
CA has terrible sheep odds.
New Mexico has low sheep odds but great hunts if you're drawn, no points but need to upfront tag fees.
Texas has sheep but have to go through a guide to hunt since all are on private property. 
Mexico has sheep but you pay through the wazzu just to hunt.
Alberta, Yukon, Northwest Territories all have sheep and goat but you need a guide as in BC and Alaska.

[WDFW-SUX]

The unlimiteds are looking better and better the way odds are exploding..

[jackelope]

I forgot about the unlimiteds. *censored* all ....

[Bob33]

You gotta be (a) rich, (b) damn lucky, or (c) patient to hunt sheep or goats.  Take your pick.

[Bob33]

Oregon sheeps odds are not very good.  They used to be better.  There were five tags available to non-residents this year.