I'm not saying in anyway you have to use grid/minis to play the game, you can sure play the old pen & paper way, but doing so will make it an hella much harder. I have a lot of reasons to say so
D&D 1e, AD&D were just perfect without a grid. in 3.x is still fine, but grids are really usefull for spellcasters, and it also helps a lot aut with AoO (given you used them in your game)
4E is definitelly going the grid way. First of all is crystal clear the combat system resembles a board game (they actually lists movement speed in squares, rather than feets, wich should stink quite a bit)
* the encounters will be much crawded (X players vs X monsters, rather than X players vs a few monsters), so say 4 players/4 mobs every other encounter. or if you're going with the minion creatures (wich will happen quite often) it gets even worst, 4 players/8 minions/2 mobs or 4 players/16 minions.
* a lot of powers "pushing the enemy x squares around"
generally more dynamic combat (rather than sticking to your chsen foe and attacking one another until he dies)
* additional movement actions triggered by other powers
* traps around the encounter location (rarely seen in previous editions)
* different terrain types
* powers wich actually modify the terrain type (not seen at the previews, but WotC actually talks a lot about that)
* Keeping track of various things for all the players and mobs (bloodied status, marks, ongoing effects, death tokens)
god, now I know why they leaved summon spells from the spell lists.
Maybe they streamlined the rules a lot, but handling the encounters is going to be a serius thing
So, can you go without a grid (graph paper can just be fine) and tokens/minis? sure you can, but have luck with it ~_~ also having to drawing/erasing everything round by round is going to take quite a bit