Yes, there are actually, and it is odd that most textbooks do not discuss them. While, all but the 1st conjugation are regularly
irregular, there are some recurring themes. This tutorial I wrote goes over the irregularities of the principal parts pretty thoroughly:
http://www.textkit.com/tutorials/200309 ... id=3&tid=3
Basically...
1st conjugation is highly regular: -o | -are | -avi | -atum | (laudo, laudare, laudavi, laudatum)
2nd conjugation: -eo | -ere | -ui | -itum | (moneo, monere, monui, monitum)
3rd conjugation: -o or -io | -ere | anything that ends in -i, but usually -di or -si or -xi | anything that ends in -um, but usually -tum or
-sum | (contendo, contendere, contendi, contentum; dico, dicere, dixi (dic-si), dictum)
4th conjugation is highly regular: -io | -ire | -ivi | -itum | (munio, munire, munivi, munitum)
Unfortunately for us, there are many exceptions to every conjugation, and you do have to memorize every principal part of every verb... there is no way around it

Be grateful you are not learning Greek (unless you are) because you would have to memorize, I think, 6 or 8 parts instead of 4.
flebile nescio quid queritur lyra, flebile lingua murmurat exanimis, respondent flebile ripae