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There are two types of special right triangles that you'll need to know: the 45-45-90 and the 30-60-90. Both are depicted below:
The ratios of the sides are worth remembering: a lot of times, problems may ask you sin(30o) or sin(/6) and expect you to come up with an exact answer without a calculator.
Pythagorean triples are sets of three numbers that fulfill the pythagorean thereom (a2+b2=c2). Tripes include 3,4,5; 5,12,13; 7,24,25; and 8,15,17. You can also attain more triples by multiplying each set by a scale factor. To find more triples, take an odd integer, square it, and halve the result. The numbers 0.5 greater than and less than the halved square will be two of the triples, and the original odd integer will be the third.
More practice problems can be found here.