The short answer is "no." If your neighbor or the mailman knocked on your door and asked to look through every drawer and inmate area of your home, you would think he was crazy and slam the door shut. Likewise, if a BMV agent asked to search your car when you went to renew your license, you would refuse. Why then would you voluntarily let a police officer search your home or car just because he asked?
The most common reason people consent to a search is because they believe they will get in trouble if they say no. The fact is that you have a constitutional right to say no to any request to search, and it is a right you should exercise. Individuals also consent to a search because they feel pressured or intimidated. Often the police will say that if you do not consent that they will have to detain your car until the "drug dog" arrives or that they will go harder on you if they have to get a warrant. The fact is that if the police ask for your permission to search your home or car, it is probably because they do not have the legal right to do so without your consent. Do you really think they are going to "let you go" just because you were nice enough to not make them do their job?
Often requiring the police to establish probable cause to search leads them to either skip the headache or conduct an unconstitutional search instead. If you think the police conducted an unlawful search of your home or car, you should contact an experienced criminal defense attorney to review the facts of the case and determine if the warrant search was legal.