If you're in the US and have an Amateur license, you can generally transmit with up to 1500 watts PEP (Peak Envelope Power). Some lower limits apply; for example a Technician licensee is limited to 200 watts in the HF bands, but may use the full 1500 watts in most VHF/UHF bands.

There is no legal distinction between a handheld and any other kind of transmitter. A transmitter is a transmitter.

There is a legal requirement to use the minimum power needed to carry out the desired communications, so you should not blast out 1500 watts at all times. Especially not next to your head!

http://www.arrl.org/frequency-allocations

Whether or not they're legal, they're a bad idea to use next to your head.

Higher power handheld transceivers usually feature a corded microphone to allow increased distance between your head and the antenna.