What do you and what do you not have to check for Shatnez?
http://shatnez.n3.net/ Here are a few:
Carpets/Rugs: May require testing. Wool carpets (wall-to-wall) and area rugs may be backed or reinforced with linen. Non-woolen rugs and carpets are not a problem. Services are available at most shatnez laboratories for those who wish to have their carpets tested.
Linen and Linen-look fabrics: Require testing.
Pajamas: Do not require testing.
Suits and Sport jackets, (Men's/Boy's): Require testing even 100% polyester and 100% silk suits.
Suits/Jackets (Women's): Only fully constructed suits require testing. "Linen-look" fabrics or those labeled as containing "other fibers" should be tested.
Ties: Linen and polyester ties with a textured surface ties need testing. Silk ties are generally free of shatnez, except for those from Spain (even 100% silk).
Trousers/Slacks/Pants: Those made in the USA have not been found to contain shatnez. All imported trousers should be tested. Any trousers which have a linen-look fabric should be checked, even if American made.
For more info- this site has an entire list with almost every item.
If anyone is looking for Hilchot Shatnez (in Hebrew) Yalkut.info-hilchot shatnez has the entire Yalkut Yosef Halachot. Also, it gives pretty much the same list as ST of America.
"Don't listen to the rumors. There is no need to check for Shaatnez on any article of clothing unless you're sure there's shaatnez in there. For all those who need to know.... Shaatnez according to some Rishonim requires "Shua, Tavi, and Nuz all together." We don't have that today. So according to those Rishonim, today's Shaatnez is only derabanan. When you bring a suit home, you only have a Safek Derabanan that is not "efsher levrury bekal." Or you can see it as a Sefek sefeka on a de'oraita. Same difference. The current so-called Shaatnez awareness was not initiated by Talmidei Chachamim. May sound radical. Probably because it is. "
Also, the Mishneh Halachos (7:198) writes similarly that without any indication on the label that there is shatnez, there is no need to be machmir and check for shatnez.
I think generally speaking, if you'd reasonably believe it could contain wool or linen.
I heard something about baseball mitts being a problem? Anyone hear of this?
From what I've heard, a garment that's entirely cotton and/or synthetic is incredibly unlikely to contain both wool and linen (but men's suits could still have lining or padding or the like ...?). Usually what people have checked (again, if I understand correctly) is clothing claiming a certain percentage to be either "wool", "linen", or "other" (which could be anything).
I think the accepted opinion holds that by an issur one should be choshesh for a "miut ha'motzoi", which I think R.H. Schachter defines as around 10%. So if you think the suit has a greater than 10% chance of being shatnez, you should get it checked. If so, I think only certain higher-end wool suits would be an issue. Some might hold one should check it even if its not a "miut hamotzoi" if its something that's very easy to do. Either way, once one suit from a line was checked, I don't see why there's any reason to check other ones. Its extremely unlikely that the manufacturer made a sudden change in the production of the same suit. So if there was a list of kosher suits, one could just check that.
There exist various guides online which answer the question. This guide, from the Hakhel website, seems to be the most complete English-language guide online. It includes a detailed chart plus four pages of color photos. It's definitely more complete than the guide which Hacham Gabriel linked to in his answer above.
When in doubt, CYLOR. The shatnez tester in my city once told me that, in cases of doubt, it's best for each person to ask his own decisor. If the decisor is unsure, he will refer the querent to the local shatnez tester.
Regarding sefek sefeka of d'Oraissa, not every machlokes haposkim will create a valid sofek. Furthermore, the actual presence of detectable issur may not be a classical sofek at all. This is not like taref ingredients which are mixed in and undetectable except to a sophisticated palate.
Mi'ut ha'matzui is appropriate here, according to many poskim. Treifos, and insect infestation, are similar cases.
How is a few dollars added to the cost of a $200+ garment not 'efshar l'vrurei b'kal?
Iirc, suits from the same line, bought off the same rack, have been found to have different threads, or collar stiffeners, etc. The factories are not particular about these things, they use whatever is available, and can 'mix and match'.