Can cell phones/laptops cause cancer radiation?

Certainly laptops do not present a danger, unless they have wireless capability, in which case the danger is very low and unlikely to cause any issues.
With respect to mobile phones, there is no doubt in my mind and educated experience with radio frequency (RF) transmissions, that there are possible adverse effects that these devices have on human tissue. It is still early days and time will tell as it did for smoking, asbestos related products and countless of chemicals and herbacides, in the past.
The simple fact is that everyone should be aware that the longer you use the phone the greater the adverse affects are likely to be. There is no doubt whatsoever, and it is well documented that high levels of RF are DANGEROUS! Cell phones transmit at much lower energy levels, but their consistant and prolonged use may well have a cumalitive effect.

Although there is no proof to indicate that mobile phones can cause cancer, there is sufficient debate to cause doubt as to the relative safety. As a telecommunications engineer I am aware of the power density levels produced by mobile phones and the effect they can have on different people.
Mobile phones transmit using radio frequency radiation (RFR). Dependant on the network this can range between 800MHz and 2GHz. These are radio waves located within the electromagnetic spectrum. X-rays which are known to cause cancer through ionizing radiation are also within the electromagnetic spectrum, however, RFRs cannot cause cancer in the same way as x-rays because RFRs are non-ionizing.

However, high levels of RFRs can cause health effects through heating the human body (thermal effects). To address this health effect, the Radiocommunications (Electromagnetic Radiation Human Exposure) Standard 1999 specifies limits on public exposure to RF radiation from mobile phones. The limits set by this Standard are only a fraction of the levels needed to cause thermal effects.

Whilst it cannot be shown at this point in time that the thermal effects from mobile phones are a health hazard there is a considerable body of scientific literature which describes the effects of RFR in biological systems that cannot be directly attributed to heating. These effects are referred to as non-thermal and have been demonstrated to cause alteration in animal behaviour, or changes in the functioning of cell membranes.

Should you wish to have a bit more reading on the subject from a non-engineering perspective, the following Cancer Council link may be of interest