Essentially, the Shinsengumi was a police troop, patrolling the streets of Kyoto and keeping the peace. They vowed to protect Kyoto with their swords. In the heat of the Ishin movements, Shishis flowed over to Kyoto to plot the downfall of the Shogunate. Add the radical actions of the Shishis, such as setting fires to the gaijin's abodes (this was done by Takasugi Shinsaku, Katsura Kogorou/Kido Koin. Takasugi is the guy who set up the Kiheitai, and in RK, the guy who first introduced Kenshin to Katsura.), and it made roshis other than Shinsengumi, especially those who'd deserted their hans, very suspicious and dangerous persons in Kyoto. So if you cannot produce a satisfactory identity, i.e. your name and your han when questioned by the Shinsengumi members, chances are that you'd be cut down at once. To quote Kenshin, in the Bakumatsu times, Kyoto was a hell where people died and blood flowed every single day. This made the Shinsengumi feared by many indeed, especially Hijikata, for he was strict and merciless, both when it comes to punishments and cutting down suspicious persons.
Their favourite combat style was many-against-one(or a few), and this became more evident as the size of the Shinsengumi increased. If the first layer of Shinsengumi members surrounding suspicious persons got cut down, further layers of members will converge on them, until they are totally exhausted and cut down. Quoting Kaoru and Kenshin, "but isn't that a coward's way, to have many on one?" Well, their main aim was to ensure the peace of Kyoto, so the method's not so important to them."