Do not walk around at night, and make sure that your car doors are locked when you drive around. Rape and armed robbery are common and on the rise. Hotels etc have private guards and are rather safe.
There are some gangs of former combattants, armed with machetes, who walk around poorer areas of Monrovia (Redlight). There are also former combatants in the Palm Grove Cemetery on Center Street. Do not walk there alone at all.
The corner of Randall and Carey is also considered dangerous and supposedly a hang-out for drug dealers.
Avoid any desolate places, and stay in groups.
Keep an eye on the locals, if they are carrying on as normal and you see plenty of women and children about, it is unlikely that there will be major sources of concern. If, however, people have disappeared from a usually busy location, or you find yourself surrounded only by youths, you should try and make a hasty retreat.
UNMIL has calmed the country (in general) but it is already now anticipated that when UNMIL leaves the security situation will be worse.
It is advisable to inform you Embassy that you are in the country in case of evacuation.
Furthermore, learn as much about the security situation as you can. Locals are a key source of information. Be careful, however, not to believe everything you hear. Rumours spread like wildfire in Monrovia as they are the main source of news. Details, however, are often inaccurate.
Local newspapers are interesting reads. Daily Observer has the largest circulation but there are also several others. You can buy them from the street.
Rape is on the increase so be hesitant to walk by yourself in previously unknown or remote areas. Men on the whole will treat women with respect. They may tell you how beautiful you are, that they love you or ask you to marry them (more for the status rather than the money), but will not grab hold of you or be in any way improper.
HIV, while still low, is on the increase. Prostitution is rampant. Typhoid, malaria, and worms are very common. In general Liberia is a hotbed for infectious diseases so disinfectants and gels are advisable (especially as handshakes are the norm). There are few doctors usable by international travellers so getting medical help may pose problems. There is apparently a Jordanian wing at the Kennedy hospital for private patients. MSF will also see a traveller, but only in dire cases.