Can I use regression to predict a binary variable based on 35 variables? I try to build a model behind a dating website which gives an optimal match between two people, based on 35 variables such as:


*

*age  

*location  

*interests  

*characteristics  

*car yes/no  

*etc  


My idea is to start with weights based on expert judgment. For example we give Age a high weight (20%) and Location a high weight (20%).
When the website is live, the data starts to be collected. For purpose of measurement, the definition of a positive outcome is a mail contact between two people. I can count the percentage positive results for every variable. For example let's say that in 82% of the contacts, the Age difference is less than 5 year. And in 37% of the contacts, the Location is within 25 kilometers. Now I can conclude Age is more important than Location and I can give Age a higher weight than Location in the model.
To optimize the exact weights of each variable in the model, I was wondering if a multiple regression would be the best method for this optimization. Or is 35 independent variables too much for a multiple regression and is there a better method?
 A: Multiple regression can handle as many independent variables as you like, but with an increasing number of regressors you need an increasing amount of data to obtain reliable estimates. 
However, for modelling binary outcomes like {match, no match} or {1, 0}, you need to transform the fitted value from a linear regression to fit in between 0 and 1. Then you can interpret it as a probability of a match conditional on the regressor values. Linear regression + transformation will give you models like logit or probit. Any reasonable statistical package should have those implemented, so they should be no more difficult to run than a simple multiple regression. One introduction to probit and logit modelling can be found here.
A: An ordinary multivariate linear regression would not apply here since your output variable is binary.  I would recommend using Regularized Logistic Regression.    L2 regularization will probably work in your case since you don't expect sparsity (all the variables ought to contribute something to the model).
Any multivariate regression model can handle an arbitrary number of features.  The important point to consider is whether you have enough data to train it reliably and avoid over-fitting.  If your website is just launching, you probably won't have enough data for a while.  Regularization will help keep the model from overfitting early on.
Just a note for the future: if you end up using this model to recommend matches, you'll be biasing your data from that point on.  So down the road, you may want to take that into consideration.
A: If I'm understanding your question correctly, it sounds like you want to figure out which combination/weighting structure of your 35 independent variables best explains an outcome (match/no match). To me, at least, this sounds like a job for a redundancy analysis. RDA is kind of like a multivariate form of regression that us ecologists use a lot when we have a lot of variables and only a vague sense of how they might all be relatively important. They are pretty simple to implement in R.
library(vegan) #This package may need to be installed if you don't already have it.
rda1 = rda(match ~ age + location + interests + ...) #Looks a lot like a linear regression.
plot(rda1) #Returns a triplot of the data -- interpreting these is an artform.
summary(rda1) #prints a lot of information about the results of the RDA.

My intuition tells me that the loadings on the first (or more) component(s) for the right side of the formula above (i.e. for your explanatory variables) could reasonably be used as weights in your algorithm of interest. These loadings will be shown in the summary, but they can also be extracted and stored seperately; see here for some details on that.
Unfortunately, like most ordinations, RDAs are much easier to run than to interpret. You can try here and here for more information, but they're both ecology-focused. It's important to point out that RDAs are not much of a conceptual leap past a principal components analysis, for which there is tons of good literature out there. Perhaps someone else here can build on my answer to help you more. To amoeba's comment, the advantage this approach would have over a linear regression is that an ordination technique like RDA will not be troubled by the number of variables you have because it is not trying to fit parameters (at least not in the same sense as a linear regression would). It's particularly good at figuring out which variables are unpredictive, as well as which are "redundant," i.e. effectively co-linear, without the need for a huge sample size. 
