Hecarim is a champion with strong defensive stats, good base damage, and average AD ratios, which means he doesn't benefit very much from items that provide raw AD. Because of this, he is most of time played as an off-tank, with armor penetration and Spellblade items as his offensive options.
Hecarim can be played as a full-tank, but this is usually not recommended, as he doesn't have enough disruption on his kit. Also, it wastes the damage potential from his skills, mainly Rampage.
Hecarim is most of time played at the jungle, due to his ganking potential with Devastating Charge, which increases dramatically after he obtains Onslaught of Shadows. Also, Hecarim has the sustain and mobility needed to effectively clear jungle camps and gank when needed. Because Hecarim is somewhat mana hungry, having easy access to the blue buff is an amazing asset for him.
That does not mean Hecarim can't used at other lanes. He is also played at top lane, although this is very rare. Hecarim should be conservative until he obtains items like Sheen and/or Glacial Shroud, otherwise he is at risk of being out of mana quickly. Still, the main reasons why Hecarim can be used at top lane, is because of the better gold influx, and the fact that Hecarim counters some popular top laners. While he loses some of his ganking potential by going top lane, he can still make surprise ganks at mid lane. Also, thanks to his Devastating Charge, Hecarim isn't easy to gank (he can even use his Onslaught of Shadows to escape if necessary). His late-game is mostly the same as his jungler counterpart.
It is important to not that independent from whether Hecarim chooses to go top or jungle, he is one of the few bruisers that doesn't fall off late game. In fact, Hecarim has amazing teamfighting potential.
Boots of Mobility has more limited usefulness because Hecarim can use Devastating Charge to effectively traverse the map without them and entering combat nullifies their bonus movement speed; however, they can still provide an extra burst of damage on your first attack.
Boots of Swiftness can be all the speed increase Hecarim needs to nearly maximize Warpath by increasing his base speed from 345 to 405, 10 points under the first soft cap. They also reduce the effectiveness of slows and allow for a more versatile itemization. A single Greater Quintessence of Movement Speed can be used to bring it to 411 movement speed, without using masteries.
Homeguard is very useful for Hecarim when defending the base because he can surprise his opponents by activating Devastating Charge at the spawning pool and dash to the pushing enemies. If you can time your Rampage just before the enhanced autoattack, you can deal a high burst of damage even when you build a few offensive items because Warpath converts your bonus movement speed into bonus AD.
Your AD can reach over 350 in a short time by using the method shown above.
Since Spirit of Dread returns health from ANY damage done to enemies while it is active, Sunfire Cape makes a better-than-usual item, essentially granting up to a bonus 52.5 health regen/5 seconds for each nearby enemy champion (with enemy minion health drained being capped) for 4 seconds, in addition to the bonus armor and health.
Sheen and Iceborn Gauntlet synergize particularly well with Rampage, as its low cooldown allows you to proc the bonus damage and slow approximately every other autoattack.
Hecarim is a powerful AoE threat, especially in the later stages of the game. Try to prevent him from itemizing. In addition, spreading out will reduce his effectiveness by preventing him from terrifying your team with Onslaught of Shadows, mitigating the constant AoE damage Hecarim can deal with Rampage, and decreasing the amount of sustain he can gain from Spirit of Dread.
Spirit of Dread grants Hecarim very high sustainability, but has a fairly lengthy cooldown and a short duration. Consider using burst damage or waiting for Spirit of Dread to time out before targeting him.
Hecarim is exceptionally weak at dueling against most champions early game, so he is susceptible to early invades from the opposing jungler. He is also incredibly reliant on Crest of the Ancient Golem, which can especially hinder his clear times should he lose the buff.