Yes, all cells contains the same genome. This is because, for a given individual, all of its cells comes from the zygote, a singular cell formed after fecondation of the maternal ovum and paternal spermatozoa, through repeated cell division (mitosis). This is a process which replicates quite exactly the genome that will be passed to the newly formed cells.
There are some exceptions however, such as :
Red blood cells, and platelets : these cells lack a nucleus, and don't contain DNA at all.
Cells bearing mutation(s) : even though the replication machinery try to make an exact copy of the DNA, error(s) may happens.
Gametes : ovum and spermatozoa are produced through meiosis, a specific replication mechanism that keeps only half the genome, and may produce new sequences through recombination.
Lymphocytes undergo V(D)J recombination and somatic hypermutation which alters their DNA, a process that is necessary to the working of our immune system.