The kashmirstamps Web site will tell you all you need to know about forgeries of Jammu & Kashmir. If you have any of the Circular types, the most common (and dangerous) are the so-called Missing Die types:

(Genuine on the right; 'Missing Die' on the left)
These are so called because, for many years after they appeared, they were thought to have come from missing dies. In fact, they were probably made by corrupt State postal officials, who made good imitations of the real things, and inserted them into the official supplies, thus doubling their money when they removed the genuine stamps.
Across the entire range of Indian States, the most common types of fakes are what are sometimes known as the Allahabad forgeries, from the town they originated in. They can fool you if you're not familiar with the originals - but once you've seen the real thing, they're obviously false.
Here are some examples from Alwar State:


and the real thing:

The Allahabad forger doesn't seem to have a perforating device, so a very easy test is: if the stamps should be perforated, but aren't, they're most likely Allahabad forgeries.
Another old
ebay favourite is the 1921 1 Anna postal-fiscal of Charkhari State:

The give-away here is that - whatever their other shortcomings - the Charkhari printers at least knew how to spell POSTAGE:

In fact, Charkhari State has come in for far more than its fair share of forgeries. This type of large double-ring CDS on a Charkhari stamp

usually means forgery.
Also beware of any stamp (not just the Indian States, of course) worth more used than mint. This Jasdan stamp

is worth £38 mint, but £275 used (2015 catalogue values). The image was taken from a well-respected German auction catalogue of a few years ago. The stamp (and another similar) sold, despite having 'postmarks' of Bandikui in Jaipur State, a complete impossibility for a stamp from Jasdan.
There are a few - very few - rare forgeries of the Indian States. This Bundi 'Sacred Cow' 12 Anna

is one. To a specialist, it would be worth as much as a genuine stamp; (hint: the dimensions are wrong). The rare and valuable fakes are valuable because they're very, very rare. You're not likely to have one. The Jammu & Kashmir 'Missing Die' forgeries sell - when they
do manage to sell at all - for a dollar or so each. Specialists in Jammu & Kashmir have them all already.
A good catalogue is vital. There's really only one choice, a Gibbons Part 1/Commonwealth & British Empire Stamps or an India sectional catalogue. A special word about the stampworld Web site, which I know many here use:
don't. It's very poor on the Indian States, and will only mislead you. If you have any OK/fake questions about the Indian States, post them here, and I'll try to answer them for you.