What distance method to use in this scenario? I have a 10 dimensional space which contain points that contain a 1 or 0 . 
example of two points : 
point1 : 1,1,1,0,0,0,1,1,0,1 
point2 : 1,0,1,0,0,0,1,0,0,0

Which distance function should I use for this. I've been trying Euclidean and Manhattan but I don't which one has an advantage over the other ?
This is binary data (1=present, 0=absent) to indicate what links are associated with a user.
For example the first binary digit might indicate that a user has www.google.com configured or not.
The clusters of links will each contain users links. For each cluster I want to recommend any link which one user has added but the other has not, this is just for users within the same cluster. So I guess this is a recommendation system based on k-means clustering.
 A: It sounds like what you're trying to achieve in this problem is unsupervised feature based clustering, where each of your 10 "dimensions" (AKA features) are observed in a sample of individuals. This is often used to form recommender systems, such as in the Netflix data where each feature was a movie rating and each row was a viewer. The goal of such models is to predict one or more features in a randomly observed individual for which some subset of features are observed.
You'd be surprised how often Euclidean based distance functions are used to create predictions from such data, as is the case with SVD and PCA. Conversely, a dearth of less obvious clustering algorithms have proven to be useful despite not giving any explicit distance measures. In both cases, models are usually validated using measures of classification accuracy (PPV, Sens/Spec eg) in split sample validation. So if you use distance to measure prediction uncertainty, it will not tell you much.
A: For presence / absence data there are various more appropriate metrics than Manhattan and Euclidean, which are really designed for continuous variables.
You really need to read up on Tanimoto, Jaccard, Gower, Cosine, Sørensen-Dice, Hamming,  Kulczyński, Czekanowski, Horn, Renkonen, ... just to name a few.
There is a pretty good book to see the variety of similarity functions that exist:

Dictionary of Distances 
Elena Deza and Michel-Marie Deza 
ISBN: 978-0-444-52087-6

