I want to get married at the end of this month, but my parents are against it because they need the money they would get for claiming me on their taxes. Could they still claim me for this year?

Perhaps - if you meet all the dependency requirements, and if you yourself don't file as "Married Filing Jointly," and you don't claim any of your own dependents then they could claim you. The dependency requirements are:

1. You must be under age 19 at the end of the year, or under age 24 if a full time student, or any age if you are disabled,
2. You must have lived with your parents for at least half the year,
3.You must not have provided more than half your own support.

Even if you meet all these requirements it may still not make sense to have your parents claim you as a dependent - the problem is that since you and your wife can't file jointly the two of you would probably end up paying more tax than you need to. The extra you would pay may well be greater than what they save: it all depends on your income, your wife's income, and your parent's tax bracket.