Communications: Never communicate more than once under the same identity. Do not use a cell phone. Borrow other people's phones, Skype, or use public phones if you need to make or receive a call. Never communicate with anyone whose inbound calls may be monitored. Use one time pad encryption where possible. Otherwise, fall back to public/private key.
Finance: Cash is king. Use prepaid disposable credit cards or stolen credit cards if you need to make a credit card transaction. If you have access, use an informal exchange system such as the much famed Islamic system. To move money internationally, buy and sell expensive items such as art or jewellery that you can carry on your person as you travel.
Travel: Boats still seem a very good option for international movement across oceans. If no ocean is involved, catch public transport that does not require leaving your identity and movements on databases (eg: unreserved trains, buses). Stolen vehicles are preferable to registered ones, obviously.
Other: You can also assume other people's identities by stealing their identity papers/other documents. It seems these days this is getting much harder as 'identity theft' countermeasures are put in place.
