If you are comprehensively insured then you can claim for personal losses to your property and compensation for certain injuries even if the accident was your fault, though if you only have third party cover and the accident can be attributed to you, then your personal losses are not covered.
Assuming that you either have comprehensive cover or you have third party cover and you can show that the accident was not your fault, the things that you can claim for include the cost of repairing, or if written off replacing, your vehicle; loss of its contents (subject to certain limits); compensation for injuries including loss of earnings; cost of transport, which might involve car hire, while you do not have use of your vehicle; and medical expenses.
If you have comprehensive cover and the accident was not your fault, then you should be able to claim from the other driver any excess charges you need to pay on your insurance. If you properly scrutinise a policy you can find budget car insurance which is still comprehensive. With third party cover if the accident was due to you then you cannot claim any of the above. Your passengers can claim for their losses as can the other drivers and their passengers, but you get nothing even if your vehicle is written off. This also applies if the accident was a so-called non-fault accident, meaning that neither driver is to blame. In order to make a claim you must demonstrate that the other driver is at fault. This can be very difficult, so often it is worth using a solicitor.