A simple question with an amazingly complex answer.
I'm not a chemist or a biologist, but I will venture an explanation based upon what I have read. According to Ian Musgrave (1), first there were simple chemicals, then those simple chemicals formed polymers, then replicating polymers, then protobiont then bacteria and the rest is history.
In your question you asked if I believe in "spontaneous generation." I believe in abiogenesis, not "spontaneous generation." Spontaneous generation was the idea that life, namely fully formed organisms, emerge from meat, and other decaying matter. That hypothesis was falsified by Pasteur a long time ago. Abiogenesis, on the other hand, is a different hypothesis which states that inorganic matter, given time, will generate organic matter, the difference being time and conditions. No, maggots do not crawl out of meat, but chemicals will form polymers which lead eventually to bacteria.
OK, so what does that mean? Through a directed, natural, process of chemical reactions, a chain of events occurred such that a simple set of chemicals were able to slowly and progressively advance to a more complex system, leading inexorably to a living organism. The Creationists mis characterize this process by saying that chemicals POOF turned into bacteria in one step (that is "spontaneous generation"), when in fact, that is not what the abiogenesis theory suggests. Indeed, it would be impossible for chemicals to magically form organized living organisms in one single step, such as maggots crawling out of meat, but that is not what happened. Other strawmen arguments follow a basic pattern. Some common ones are;
1) If you lock a closed room and come back a million years later, it will not be organized. (Assuming the house is still standing, no, you would not. Just another "spontaneous generation" example.)
2) If you leave a bathtub full of water for a million years, it will not have a fish in it. (The water would have evaporated in the first week.)
The picture to the right, which outlines the two conflicting assessments of the origins of life, was taken from an article written by Ian Musgrave. Musgrave outlines 5 of the most common misconceptions of the abiogenesis debate;
”1) They [creationists] calculate the probability of the formation of a "modern" protein, or even a complete bacterium with all "modern" proteins, by random events. This is not the abiogenesis theory at all.
2) They assume that there are a fixed number of proteins, with fixed sequences for each protein, that are required for life.
3) They calculate the probability of sequential trials, rather than simultaneous trials.
4) They misunderstand what is meant by a probability calculation.
5) They seriously underestimate the number of functional enzymes/ribozymes present in a group of random sequences.” (1)
After the first Miller-Urey experiment, abiogenesis moved out of the realm of hypothesis and into the realm of testable science. They found that if an evaporated solution of H2O, CH4, NH3, and H2 were subjected to electricity, organic compounds formed after only one week. According to the theory several million of these "experiments" were conducted by natural processes to form the first polymer. Current theories suggest that these compounds must be shielded from UV light, perhaps near a deep sea vent. Feldspar, the most common rock on earth, may have been a catalyst as well.
In conclusion, there is a difference between spontaneous generation and abiogenesis. Spontaneous generation was falsified, whereas abiogenesis is robust area of scientific investigation. Creationists, in a straw-man argument, try to criticize abiogenesis, when in fact, they are arguing against the already falsified hypothesis of spontaneous generation.
Thank you, Matthew, for the question.
Genesis: The Scientific Quest for Life's Origin. By Robert M. Hazen
Easy-to-Read article by Hazen;
more difficult article by Dr. Robert Hazen
Talk origins section on abiogenesis